Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the distance of the point $(i^+2j^ +5k^)$ from the plane $r⋅(i^+j^ +k^)+17=0$.

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

Equation of a line in the plane $π=2x−y+z−4=0$ which is perpendicular to the line $l$ whose equation is $1x−2 =−1y−2 =−2z−3 $ and which passes through the point of intersection of $l$ and $π$ is (A) $1x−2 =5y−1 =−1z−1 $ (B) $3x−1 =5y−3 =−1z−5 $ (C) $2x+2 =−1y+1 =1z+1 $ (D) $2x−2 =−1y−1 =1z−1 $

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

Find the equation of a line which passes through the point $(1,1,1)$ and intersects the lines $2x−1 =3y−2 =4z−3 and1x+2 =2y−3 =4z+1 ˙$

The intercept made by the plane $rn˙=q$ on the x-axis is a. $i^n˙q $ b. $qi^n˙ $ c. $qi^n˙ $ d. $∣n∣q $

If the sum of the squares of the distance of a point from the three coordinate axes is 36, then find its distance from the origin.

Find the direction ratios of orthogonal projection of line $1x−1 =−2y+1 =3z−2 $ in the plane $x−y+2z−3=0.$ also find the direction ratios of the image of the line in the plane.

A parallelepiped is formed by planes drawn through the points $P(6,8,10)and(3,4,8)$ parallel to the coordinate planes. Find the length of edges and diagonal of the parallelepiped.