Practice Test

Q1) If a line is equally inclined to co-ordinate axes, then its each direction angle is of measure Show Answer

Q2) Direction cosines of a line, whose direction ratios are -2, 1, 2 are Show Answer

Q3) If P is (-1, 1, 2), then direction cosines of line OP are Show Answer

Q4) Direction cosines of the line passing through A(2, 3, -1) and B(-3, -4, 2) are Show Answer

Q5) If the join of A(4,1, 2), B (5, b, 0) is parallel to the join of C(2, 1, 1), D(3, 3, -1), then b = Show Answer

Q6) If l, m, n are direction cosines of a line then vector li + mj+ nk is a Show Answer

Q7) Angle between lines whose direction ratios are 1, 2, 1 and 2, -3, 4 is Show Answer

Q8) If direction ratios of two lines are 2, -6, -3 and 4, 3, -1, then direction ratios of a line perpendicular to them are Show Answer

Q9) Number of lines in space which are equally inclined to three co-ordinate axes are Show Answer

Q10) Projection of the line segment joining the points (-1, 0, 3) and (2, 5, 1) on the line whose direction Ratios are 6, 2, 3 is Show Answer

Q11) Direction Cosines of a normal to the XOY-plane are Show Answer

Q12) A mirror and a source of light are situated at the origin O and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are 1, -1, 1, then direction ratios of the reflected ray are Show Answer

Q13) l=m=n=1 are the direction cosines of Show Answer

Q14) If P(x, y, z) is a point in space at a distance r from the origin O, then direction Cosines of the line OP Show Answer

Q15) Co-ordinates of the foot of the perpendicular from the point (a, b, c) on the Z-axis are Show Answer

Q16) In three dimensional space, the equation xy = 0 represents Show Answer

Q17) In space, the equation 3x - 4y = 0 represents Show Answer

Q18) Equation of the line passing through the point (0, 1, 2), and equally inclined to the co-ordinate axes, are Show Answer

Q19) Equations of line joining (2, -3, 1) and (3, -4, -5) are Show Answer

Q20) Equations of line joining (1, 2, 3) and (-3, 4, 3) are Show Answer

Q21) Equation of the line passing through (a, b, c), and parallel to Z-axis are Show Answer

Q22) Equation of the line passing through (a, b,c) and perpendicular to Z-axis are Show Answer

Q23) Equations of the line passing through the origin and the point (a, b, c) are Show Answer

Q24) Line joining the points (2, -3, 1) and (3, -4, -5) intersects the plane 2x + y + z = 7 in the point Show Answer

Q25) Co-ordinates of the foot of the perpendicular drawn from the origin to the plane 2x + 3y - 4z + 1 = 0 are Show Answer

Q26) Measure of angle between the lines 3x + 2y + z - 3 = 0, x + y - 2z - 3 = 0 and 2x - y - z = 0, 7x + 10y - 8z = 15 is Show Answer

Q27) Distance of the point (1, -2, 3) from the plane x - y + z = 5, measured parallel to the line whose direction cosines are proportional to 2, 3, -6 is Show Answer

Q28) Equations of the line of intersection of the two planes y = b, z = c in the symmetrical form are Show Answer

Q29) Equation of plane passing through A (0, -1, 3) and perpendicular to the join of A to B (1, 3, 5) is Show Answer

Q30) Equation of plane passing through (2, 6, 1) and perpendicular to the join (-3, 1, 2) and (4, -3, 6) is Show Answer

Q31) Equation of plane which bisects the join of A (3, 7, 12) and B (-5, -3, -2) at right angles is Show Answer

Q32) Equation of plane passing through P (a, a, 0) and normal to OP is Show Answer

Q33) Equation of plane passing through A (a, b, c) and normal to OA is Show Answer

Q34) If perpendiculars from the point P (a, b ,c) drawn to Y Z - and Z X - planes meet them in the points L and M respectively, then equation of plane OLM is Show Answer

Q35) Equation of plane passing through (0, 0, a) and perpendicualr to two planes x - y - z = 0 and x - 2y = 0 is Show Answer

Q36) Equation of plane passing through (-1, -1, 2) and perpendicular to two planes x - 2y + z = 4 and x + 2y - 2z + 4 = 0 is Show Answer

Q37) Equation of plane, passing through (-1, 3, 2) and perpendicualr to two planes x + 2y + 2z = 5 and 3x + 3y + 2z = 8 is Show Answer

Q38) Equation of plane passing through two points (-1, 2, 0), (1, 1, 2) and perpendicualr to the plane x + 2y + 2z = 4 is Show Answer

Q39) Equation of plane passing through two points (-1, 1, 1), (1, -1, 1) and perpendicular to the plane x + 2y + 2z = 5 is Show Answer

Q40) Equation of plane passing through (0, -2, 3) and containing the X - axis, is Show Answer

Q41) Equation of plane passing through (4, 0, 3) and containing the Y - axis, is Show Answer

Q42) Equation of plane passing through (2, -4, 0) and containing the Z - axis, is Show Answer

Q43) Equation of plane passing through two points (0, 1, 3), (2, 4, 5), and parallel to X - axis, is Show Answer

Q44) Equation of plane passing through two points (2, 3, 1), (4, -5, 3), and parallel to Y - axis, is Show Answer

Q45) Equation of plane passing through two points (2, 2, 0), (4, 0, 0), and parallel to Z - axis, is Show Answer

Q46) Equation of plane passing through two points (2, 2, 1), (9, 3, 6) and perpendicular to the plane 2x + 6y + 6z = 9 is Show Answer

Q47) Equation of plane passing through three points (2, 2, -1), (3, 4, 2) and (7, 0, 6) is Show Answer

Q48) Equation of plane passing through three points (1, 1, 1), (1, -1, 1) and (-7, -3, -5) is Show Answer

Q49) Equation of plane passing through (5, 2, -1), (2, 2, 3) and the origin is Show Answer

Q50) Equation of plane passing through (1, 2, 3) and perpendicular to the vector 3i - 4j + k is Show Answer

Q51) Equation of plane passing through (2, 0, 5), and parallel to the vectors i - j + k and 3i + 2j - k, is Show Answer

Q52) Point P divides the join of A (4, -2, -1) and B (1, 4, 2) internally in the ratio 2 : 1. Equation of plane passing through P and perpendicular to line A B is Show Answer

Q53) Equation of plane passing through (1, 0, 1), (3, 1, 2) and parallel to the vector i - j + 2k is Show Answer

Q54) Equation of plane passing through (2, 1, 0), and perpendicular to the unit vector k along the Z-axis, is Show Answer

Q55) A non-zero vector parallel to the plane 3x + y - z = 2 and perpendicular to the vector i + 2k is Show Answer

Q56) A non-zero vector perpendicular to the two planes x + 2y - z + 1 = 0 and 2x - y + z + 9 = 0 is Show Answer

Q57) Measure of angle between the planes 5x - 2y + 3z - 7 = 0 and 15x - 6y + 9z + 5 = 0 is Show Answer

Q58) Measure of angle between the planes x + y + 2z = 3 and 2x - y + 2z = 5 is Show Answer

Q59) Equation of plane through (2, -1, 3) and making equal intercepts on the co-ordinate axes is Show Answer

Q60) Equation of plane passing through (2, 1, 3), making equal intercepts on X - axes and Y - axes, and having Z - intercept 4, is Show Answer

Q61) Equation of plane passing through (1, -3, 5), whose y - and z - intercepts are both double the x- intercept, is Show Answer

Q62) Equation of plane passing through (-4, 0, 4) and making intercepts 4 and 3 on X - axis and Y - axis respectively, is Show Answer

Q63) A plane bisects the join of (1, 2, 3) and (3, 4, 5) at right angles. Its interecetps on the co-ordinates axes are Show Answer

Q64) Length of the normal to the plane 2x - 2y - z + 3 = 0 is Show Answer

Q65) Measure of angle between the lines 2x = 3y = -z and 6x = -y = -4y is Show Answer

Q66) Equation of plane passing through (2, 3, 4) and parallel to the plane x + 2y + 4z = 5 is Show Answer

Q67) Equations of the line passing through (1, 1, 1) the parallel to the plane 2x + 3y + z + 5 = 0 is Show Answer

Q68) The XOY - plane divides the join of the points (a, b, c) and (-a, -b, -c) in the ratio Show Answer

Q69) Equation of plane passing through (2, -3, 1) and perpendicular to the join of (3, 4, -1) and (2, -1, 5) is Show Answer

Q70) Equation of plane passing thorugh (2, 3, 1) and (4, -5, 3) and parallel to the X - axis is Show Answer

Q71) Equation of plane perpedicular to the YZ - plane and passing through (1, -2, 4) and (3, -4, 5) is Show Answer

Q72) Equation of plane containing the points A (1, 0, 1) and B (3, 1, 2), and parallel to the line joining the origin to the point C (1, -1, 2) is Show Answer

Q73) Equation of plane passing through (1, 1, 1) and the line of intersection of planes x + 2y - z + 1 = 0 and 3x - y - 4z + 3 = 0, is Show Answer

Q74) Equation of plane passing through the line of intersection of planes 2x = y and y = 3z, and perpendicular to plane 4x + 5y - 3z = 8, is Show Answer

Q75) Equation of plane passing through (-1, 3, 2) and perpendicular to the two planes x + 2y + 2z = 5, and 3x + 3y + 2z = 8, is Show Answer

Q76) Equation of plane passing through (1, 1, 0), (-2, 2, -1) and (1, 2, 1) is Show Answer

Q77) Measure of angle between the lines x = 1, y = 2 and y = -1, z = 0 is Show Answer

Q78) Four points (0, 4, 3), (-1, -5, -3), (-2, -2, 1) and (1, 1, -1) lie in the plane Show Answer

Q79) Equation of plane passing through (-2, -2, 2), and containing the line joining the points (1, 1, 1) and (1, -1, 2), is Show Answer

Q80) If l, m, n are the direction Cosines of a normal to a plane passing through the point (1, 2, 3), then the equation of the plane is Show Answer

Q81) The line x = 1, y = 2 is Show Answer

Q82) Locus of the equation xy + yz = 0 is Show Answer

Q83) Measure of the acute angle between the plane 5x - 4y + 7z = 12 and the Y - axis is Show Answer

Q84) The three planes x + y = 0, y + z = 0 and z + x = 0 Show Answer

Q85) The direction Ratios of a normal to the plane passing through the points (0, 0, 1), (0, 1, 2) and (1, 2, 3) are Show Answer

Q86) If the plane x + 2y + kz = 0 and 2x + y - 2z = 0 are mutually perpendicular, then : k = Show Answer

Q87) The direction Cosines of a normal to the plane x + 2y - 3z + 4 = 0 are Show Answer

Q88) Projection of the line segment joining A (-1, 0, 3) and B (2, 5, 1) on the line whose d.R.s. are 6, 2, 3 is Show Answer

Q89) If the d.R.s. of two lines are 1, -2, -2 and 2, -2, 1, then the measures of the acute angle between them is Show Answer

Q90) If the line joining the points P (-2, 1, -8) and Q (a, b, c) is in the direction of the vector 6i + 2j + 3k, then the respective values of a, b, c are Show Answer

Q91) The d.C.s. of the line 3x - 1 = 2y - 3 = 4z - 1 are Show Answer

Q92) Equation of the plane passing through the points (1, 0, 1), (-1, 1, 1) and (2, 3, 1) is Show Answer

Q93) Equation of the plane passing through the origin, and parallel to the vectors i + 3j - k and j + k, is Show Answer

Q94) The plane 3x + y - 2z = 4 meets the Y-axis in the point Show Answer

Q95) Equation of the plane passing through the points A = (2, 1, -1), B (3, 1, 2), and parallel to X - axis, is Show Answer

Q96) If the points (3, 9, x), (-4, 4, 4), (4, 5, 1) and (0, -1, -1) are coplanar, then : x = Show Answer

Q97) XY-plane divides the segment joining the points A (2, 4, 5) and B (-4, 3, -2) in the ratio Show Answer

Q98) Equation of the plane which bisects the join of the points A (3, -1, 4) and B (-3, 5, 2) at right angles is Show Answer

Q99) If the foot of the perpendicular from the origin to a plane is (2, -3, 4), then the equation of the plane is Show Answer

Q100) If a plane makes intercepts 2, 2, 1 on X-, Y- and Z- axes respectively, then its perpendicular distance from the origin is Show Answer

Q101) A plane is parallel xy-plane, so it is perpendicular to Show Answer

Q102) The locus of a point for which y = 0, z = 0 is Show Answer

Q103) The point (- 2, - 3, - 4) lies in the Show Answer

Q104) L is the foot of the perpendicular drawn from a point P( 3, 4, 5 ) on the xy-plane. The coordinates of point L are Show Answer

Q105) The distance of point P ( 3, 4, 5 ) from the yz-plane is Show Answer

Q106) What is the length of foot of perpendicular drawn from the point P ( 3, 4, 5 ) on y-axis ? Show Answer

Q107) If x-coordinate of a point P of line joining the points Q ( 2, 2, 1 ) and R ( 5, 2, - 2 ) is 4, then the z - coordinate of P is Show Answer

Q108) Distance of the point (1, 2, 3) from the coordinate axes are Show Answer

Q109) If the sum of the squares of the distance of a point from the three coordinate axes be 36, then its distance from the origin is Show Answer

Q110) The coordinates of a point which is equidistant from the point ( 0, 0, 0 ), ( a, 0, 0 ), ( 0, b, 0 ), ( 0, 0, c ) are given by Show Answer

Q111) If a parallelopiped is formed by planes drawn through the points ( 5, 8, 10 ) and ( 3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelopiped is Show Answer

Q112) Find the coordinates of the point which divides the line segment joining the points ( - 2, 3, 5) and ( 1, - 4, 6) in the ratio 2 : 3 externally. Show Answer

Q113) Find the ratio in which the YZ - plane divides the line segment formed by joining the points ( - 2, 4, 7) and ( 3, - 5, 8). Show Answer

Q114) Find the length of the medians of the triangle with vertices A ( 0, 0, 6 ), B ( 0, 4, 0 ) and C ( 6, 0, 0 ). Show Answer

Q115) Find the coordinates of the points which trisect the line segment joining the points P ( 4, 2, - 6 ) and Q ( 10, - 16, 6 ). Show Answer

Q116) The points A ( 5, - 1, 1 ), B ( 7, - 4, 7 ), C (1, - 6, 10 ) and D ( - 1, - 3, 4 ) are vertices of a Show Answer

Q117) The points ( 5, - 4, 2 ), ( 4, - 3, 1 ), ( 7, - 6, 4 ) and ( 8, - 7, 5 ) are the vertices of Show Answer

Q118) The mid-points of the sides of a triangle are ( 5, 7, 11 ), ( 0, 8, 5 ) and ( 2, 3, - 1). Then, the vertices are Show Answer

Q119) The area of the triangle, whose vertices are at the points ( 2, 1 , 1 ), ( 3, 1, 2 ) and ( - 4, 0, 1 ) is Show Answer

Q120) If vertices of a triangle are A ( 1, - 1, 2 ), B ( 2, 0, - 1 ) and C ( 0, 2, 1 ), then the area of a triangle is Show Answer

Q121) The triangle formed by the points ( 0, 7, 10 ), ( - 1, 6, 6 ), ( - 4, 9, 6) is Show Answer

Q122) The points ( 5, 2, 4 ), ( 6, - 1, 2 ) and ( 8, - 7, k ) are collinear, if k is equal to Show Answer

Q123) The point A ( 1, - 1, 3 ), B ( 2, - 4, 5 ) and C ( 5, - 13, 11 ) are Show Answer

Q124) If orthocentre and circumcentre of a triangle are respectively ( 1, 1, 1 ) and ( 3, 2, 2 ), then the coordinates of its centroid is Show Answer

Q125) The incentre of triangle with vertices A ( 1, 1, 2 ), B ( 2, 1, 3 ) and C ( 1, - 1, 3 ) is Show Answer