Three Dimensional Geometry
If the distance between the plane Ax−2y+z=d. and the plane containing the lies 2x+1=3y−2=4z−3and3x−2=44−3=5z−4 is 6, then ∣d∣ is
Find the equation of the plane passing thorugh the line of intersection of the planes 2x−y=0 and 3z−y=0, and perpendicular to the plane 4x+5y−3z=9.
Find the vector equation of the plane passing through the intersection of the planes r⋅(2i^−7j^+4k^)=3 and r⋅(3i^−5j^+4k^)+11=0, and passing through the point (−2,1,3).
Find the value of λ for which the line 2x−1=3y−1=λz−1 is parallel to the plane r⋅(2i^+3j^+4k^)=4.
Reduce the equation 2x−3y+5z+4=0 to intercept form and find the intercepts made by it on the coordinate axes.
For the following planes, find the direction cosines of the normal to the plane and the distance of the plane from the origin.
If the equations of a line are −33−x=−2y+2=6z+2, find the direction cosines of a line parallel to the given line.