Three Dimensional Geometry questions
879 published questions with worked solutions.
- The equation of the plane containing the straight line x2 = y3 = z4 and perpendicular to the plane containing the straight lines...
- The equation of the line passing through (−4, 3, 1), parallel to the plane x + 2y − z − 5 = 0 and intersecting the line x+1 -3 =...
- The plane through the intersection of the planes x + y + z = 1 and 2x + 3y − z + 4 = 0 and parallel to y-axis also passes through...
- If the line x-2 3 = y+1 2 = z-1 -1 intersects the plane 2x + 3y − z + 13 = 0 at a point P and the plane 3x + y + 4z = 16 at a...
- Let S be the set of all real values of λ such that a plane passing through the points (- ^2, 1, 1), (1, - ^2, 1) and (1, 1, - ^2)...
- If an angle between the line, x+1 2 = y-2 1 = z-3 -2 and the plane, x − 2y − kz = 3 is ^ -1 ( 2 2 3 ), then a value of k is:
- The perpendicular distance from the origin to the plane containing the two lines, x+2 3 = y-2 5 = z+5 7 and x-1 1 = y-4 4 = z+4 7...
- A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(−1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is:
- Two lines x-3 1 = y+1 3 = z-6 -1 and x+5 7 = y-2 -6 = z-3 4 intersect at the point R. The reflection of R in the xy-plane has...
- If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the...
- The plane containing the line x-3 2 = y+2 -1 = z-1 3 and also containing its projection on the plane 2x + 3y − z = 5, contains...
- The direction ratios of normal to the plane through the points (0, −1, 0) and (0, 0, 1) and making an angle 4 with the plane y −...
- On which of the following lines lies the point of intersection of the line, x-4 2 = y-5 2 = z-3 1 and the plane, x + y + z = 2?
- The plane which bisects the line segment joining the points (−3, −3, 4) and (3, 7, 6) at right angles, passes through which one...
- The plane passing through the point (4, −1, 2) and parallel to the lines x+2 3 = y-2 -1 = z+1 2 and x-2 1 = y-3 2 = z-4 3 also...
- A plane which bisects the angle between the two given planes 2x − y + 2z − 4 = 0 and x + 2y + 2z − 2 = 0, passes through the...
- The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines r = ( i + j) + ( i + 2 j - k)...
- If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through ( , 7, 1) is ( 5 3 , 7 3 , 17 3 ), then...
- If the distance between the plane, 23x – 10y – 2z + 48 = 0 and the plane containing the lines x+1 2 = y-3 4 = z+1 3 and x+3 2 =...
- The projection of the line segment joining the points (1, −1, 3) and (2, −4, 11) on the line joining the points (−1, 2, 3) and...
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