Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the equation of the plane passing through the points $A(−1,1,1)$ and $B(1,−1,1)$ and perpendicular to the plane $x+2y+2z=5$.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Find the vector equation of the following planes in Cartesian form: $r=i^−j^ +λ(i^+j^ +k^)+μ(i^−2j^ +3k^)˙$

A plane passes through a fixed point $(a,b,c)˙$ Show that the locus of the foot of the perpendicular to it from the origin is the sphere $x_{2}+y_{2}+z_{2}−ax−by−cz=0.$

$ABC$ is a triangle and A=(2,3,5),B=(-1,3,2) and C= $(λ,5,μ).$ If the median through $A$ is equally inclined to the axes, then find the value of $λ$ and $μ$

If the lines $2x−1 =3y+1 =4z−1 $ and $1x−3 =2y−k =1z $ intersect, then k is equal to (1) $−1$ (2) $92 $ (3) $29 $ (4) 0

Find the locus of appoint which moves such that the sum of the squares of its distance from the points $A(1,2,3),B(2,−3,5)andC(0,7,4)is120.$

Find the equation of the plane which is parallel to the lines $r=i^+j^ +λ(2i^+j^ +4k^)and−3x+1 =2y−3 =1z+2 $ and is passing through the point $(0,1,−1$ ).

Find the angel between the lines $2x=3y=−zand6x=−y=−4z˙$

Find the equation of the projection of the line $2x−1 =−1y+1 =4z−3 $ on the plane $x+2y+z=9.$