Introduction to 3D Questions

Perpendiculars are drawn from points on the line the plane x + y + z = 3. The feet of perpendiculars lie on the line...

Consider the lines L1 : L2 : and the planes P1: 7x+y + 2z = 3, P2 : 3x + 5y - 6z = 4. Let ax + by + cz = d be the equation of the plane passing through the point of intersection of lines L1 and L2 and...

An equation of a plane parallel to the plane x-2y + 2z - 5 = 0 and at a unit distance fromthe origin is :

If the lines and intersect, then k is equal to:

The point P is the intersection of the straight line joining the points Q(2, 3, 5) and R(1, -1, 4) with the plane5x - 4y - z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1, 4) ...

The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x - y + z = 3 and at a distance from the point (3, 1, - 1) is...

A line with positive direction cosines passes through the point P(2, - 1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line...

The plane XOZ divides the join of (1, -1, 5) and (2, 3, 4) in the ratio λ : 1, then λ is -

Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the area of triangle ABC, ACD and ADB be 3, 4 and 5 sq. units respectively. Then the area of the triangle BC...

Which one of the following statement is INCORRECT ?

Consider the following 5 statements(I) There exists a plane containing the points (1, 2, 3) and (2, 3, 4) and perpendicular to the vector (II) There exist no plane containing the point (1, 0 0); (0, 1...

Let L1 be the line and let L2 be the line . Let be the plane which contains the line L1 and is parallel to L2. The distance of the plane from the origin is -...

The intercept made by the plane = q on the x-axis is -

If from the point P(f, g, h) perpendiculars PL, PM be drawn to yz and zx planes then the equation to the plane OLM is -

The line which contains all points (x, y, z) which are of the form (x, y, z) = (2, -2, 5) + λ (1, -3, 2) intersects the palne 2x - 3y + 4z = 163 at P and intersects the YZ plane at Q. If the dist...

A plane passes through the point P(4, 0, 0) and Q(0, 0, 4) and is parallel to the y-axis. The distance of the plane from the origin is -

The distance between the parallel planes given by the equations, + 3 = 0 and + 5 = 0 is -...

If the plane 2x - 3y + 6z - 11 = 0 makes an angle sin-1(k) with x-axis, then k is equal to -

A variable plane forms a tetrahedron of constant volume 64K3 with the coordinate planes and the origin, then locus of the centroid of the tetrahedron is -

The expression in the vector form for the point of intersection of the plane = d and the perpendicular line where t is a parameter given by -...