Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the acute angle between the following planes.$x+2y+2z=3$ and $2x−3y+6z=8$.

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Find the equation of the plane which passes through the point $(1,2,3)$ and which is at the minimum distance from the point $(−1,0,2)˙$

The equation of the plane through the intersection of the planes $x+2y+3z−4=0and4x+3y+2z+1=0$ and passing through the origin is (a) $17x+14y+11z=0$ (b) $7x+4y+z=0$ (c) $x+14+11z=0$ (d) $17x+y+z=0$

Find the equation of the image of the plane $x−2y+2z−3=0$ in plane $x+y+z−1=0.$

Find the shortest distance between lines $r=(i^+2j^ +k^)+λ(2i^+j^ +2k^)andr=2i^−j^ −k^+μ(2i^+j^ +2k^)˙$

Find the shortest distance between the lines $2x−1 =3y−2 =4z−3 and3x−2 =4y−4 =5z−5 $ .

Find the image of the line $9x−1 =−1y−2 =−3z+3 $ in the plane $3x−3y+10z−26=0.$

The pair of lines whose direction cosines are given by the equations $3l+m+5n=0and6mn−2nl+5lm=0$ are a. parallel b. perpendicular c. inclined at $cos_{−1}(61 )$ d. none of these

Find the value of $m$ for which thestraight line $3x−2y+z+3=0=4x+3y+4z+1$ is parallel to the plane $2x−y+mz−2=0.$