Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the distance of the point $(2i^−j^ −4k^)$ from the plane $r⋅(3i^−4j^ +12k^)=9$.

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Find the distance of the point $P(a,b,c)$ from the x-axis.

The distance of point A (-2, 3, 1) from the line PQ through P (- 3, 5, 2), which makes equal angles with the axes is

The point of intersecting of the line passing through $(0,0,1)$ and intersecting the lines $x+2y+z=1,−x+y−2z=2andx+y=2,x+z=2$ with xy-plane is

If the center of the sphere ax2+by2+cz2−2x+4y+2z−3=0is (1/2,−1,−1/2), what is the value of b ?

Find the equation of the line passing through the intersection of $2x−1 =3y−2 =4z−3 and5x−4 =2y−1 =z˙$ and also through the point $(2,1,−2)˙$

Find the equation of a sphere whose centre is $(3,1,2)$ radius is $5.$

Show that $ax+by+r=0,by+cz+p=0andcz+ax+q=0$ are perpendicular to $x−y,y−zandz−x$ planes, respectively.

The vector equation of the line of intersection of the planes r⃗ =b⃗ +λ1(b⃗ −a⃗ )+μ1(a⃗ −c⃗ ) and r⃗ =b⃗ +λ2(b⃗ −c⃗ )+μ2(a⃗ +c⃗ )a⃗ ,b⃗ ,c⃗ being non-coplanar vectors, is