Class 12

Math

3D Geometry

Three Dimensional Geometry

Write the equations of line parallel to the line $−3x−2 =2y+3 =6z+5 $ and passing through the point $(1,−2,3)$.

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Find the equation of the plane such that image of point $(1,2,3)$ in it is$(−1,0,1)˙$

If the lines $−3x−1 =2ky−2 =−2z−3 and3kx−1 =1y−5 =−5z−6 $ are at right angle, then find the value of $k˙$

Under what condition do represent direction cosines of a line?

Show that the plane $2x−2y+z+12=0$ touches the sphere $x_{2}+y_{2}+z_{2}−2x−4y+2z−3=0.$

Find the equation of the plane passing through the point $(2,3,1)$ having $(5,3,2)$ as the direction ratio is of the normal to the plane.

Which one of the following is the plane containing the lien x−22=y−33=z−45 and parallel to z axis?

Find the angle between the line $r=i^+2j^ −k^+λ(i^−j^ +k^)$ and the plane $r2i^−j^ +k^˙ =4.$

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