class 12

Math

3D Geometry

Three Dimensional Geometry

If the line, $2x−3 =−1y+2 =3z+4 $lies in the place, $lx+my−z=9$, then $l_{2}+m_{2}$is equal to:

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Find the distance of the point $(2,1,−1)$ from the plane $x−2y+4z=9$.

The equation of the plane passing through the intersection of the planes $3x−y+2z−4=0$ and $x+y+z−2=0$ and passing through the point $A(2,2,1)$ is given by?

Write the general equation of a plane parallel to the x-axis.

Show that the line $r=(2i^+5j^ +7k^)+λ(i^+3j^ +4k^)$ is parallel to the plane $r⋅(i^+j^ −k^)=7$. Also, find the distance between them.

The coordinates of the point where the line through the points $A(5,1,6)$ and $B(3,4,1)$ crosses the yz-plane is

Find the vector and Cartesian forms of the equations of the plane containing the two lines $r=(i^+2j^ −4k^)+λ(2i^+3j^ +6k^)$ and $r=(3i^+3j^ −5k^)+μ(−2i^+3j^ +8k^)$.

Find the angle between the lines $r=(2i^−5j^ +k^ )+λ(3i^+2j^ +6k^ )$ and $r=(7i^−6k^ )+μ(i^+2j^ +2k^ )$

Find the equation of the plane through the points $A(2,1,−1)$ and $B(−1,3,4)$ and perpendicular to the plane $x−2y+4z=10$. Also, show that the plane thus obtained contains the line.$r=(−i^+3j^ +4k^)+λ(3i^−2j^ −5k^)$.