Interaction between a Line and a Plane

IMPORTANT

Interaction between a Line and a Plane: Overview

This topic covers concepts such as Condition when a Line Completely Lies on a Plane, Angle between Line and a Plane in Vector Form, A Line and a Plane, Intersection Point of a Line and a Plane, etc.

Important Questions on Interaction between a Line and a Plane

HARD
IMPORTANT

Find the distance of the point  1, 5, 10, from the point of intersection of the line r=2i^j^+2k^+λ3i^+4j^+2k^ and the plane ri^j^+k^=5.

MEDIUM
IMPORTANT

The coordinate of the point where the line x+1 2 = y+2 3 = z+3 4 meets the plane x+y+4z=6 is

HARD
IMPORTANT

The angle between the line   x+1 2 = y 3 = z3 6  and the plane   10x+2y11z=3 would be :

HARD
IMPORTANT

If the lines   x1 3 = y2 2k = z3 2  and   x1 k = y2 1 = z3 5 are perpendicular, what would be the value of k and the equation of plane containing these lines?

EASY
IMPORTANT

The coordinates of the point where the line  x+12=y+23=z+34  meets the plane x+y+4z=6  would be:

HARD
IMPORTANT

The perpendicular distance from the point 3,1,1 on the plane passing through the point 1,2,3 and containing the line, r=i^+j^+λ2i^+j^+4k^ is

HARD
IMPORTANT

If the line x-14=y+3-2=z+51 lies in the plane 2x+ly+mz=16, then l2+m2 is equal to

MEDIUM
IMPORTANT

If planes x-cy-bz=0, cx-y+az=0 and bx+ay-z=0 pass through a straight line then a2+b2+c2=

HARD
IMPORTANT

The length of the projection of the line segment joining the points (5,-1, 4) and (4,-1, 3) on the plane, x+y+z=7 is

HARD
IMPORTANT

The distance between the point -1,-5,-10 and the point of intersection of the line x-23=y+14=z-212 with the plane x-y+z=5 is 13t, then t equals to

MEDIUM
IMPORTANT

The measure of the angle between the line r=2,-3,1+k2,2,1 ;kR and the plane 2x-2y+z+7=0 is ..

MEDIUM
IMPORTANT

The perpendicular distance from the point of intersection of the line x+12=y+23=z-1 and plane 2x-y+z=0 to the Z-axis is .

MEDIUM
IMPORTANT

Let Np,q,r represents the point where the line through 3,4,1 and 5,1,0 intersects yz-plane, then q-2r=

MEDIUM
IMPORTANT

If β be the angle between the line r=-i^+j^+2k^+λi^+2j^+2k^ and the plane r·2i^-j^+ak^+4=0 such that sinβ=13, then the value of a can be

MEDIUM
IMPORTANT

If the plane 2x  3y  6z = 13 makes an angle sin-1(λ) with the x - axis, then the value of λ is 

HARD
IMPORTANT

The angle between the line r=(i^+2ȷ^-k^)+λ(i^-j^+k^) and the plane r·(2i^-ȷ^+k^)=5 is 

MEDIUM
IMPORTANT

The angle between the plane r.i^-2j^+3k^=5 and the line r=i^+j^-k^+λi^-j^+k^ is 

MEDIUM
IMPORTANT

The angle between the line x-13=y+12=z+24 and the plane 2x+y-3z+4=0 is 

MEDIUM
IMPORTANT

If the line x-23=y-1-5=z+22 lies in the plane x+3 y-α z+β=0, then (α,β) is

HARD
IMPORTANT

If the line x-32=y-43=z-54 lies in the plane 4x+4y-kz-d=0, then find the value of k+d.