Three Dimensional Geometry
The shortest distance between line y-x=1and curve x=y2is :
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Prove that the normals to the planes 4x+11y+2z+3=0 and 3x−2y+5z=8 are perpendicular to each other.
Find the equation of the plane passing through the line of intersection of the planes x+2y+3z−5=0 and 3x−2y−z+1=0 and cutting off equal intercepts on the x-axis and z-axis.
Find the direction cosines of the line 24−x=6y=31−z.
Write the angle between the line 2x−1=1y−2=−2z+3 and the plane x+y+4=0.
Find the vector equation of the plane passing through the point (3i^+4j^+2k^) and parallel to the vectors (i^+2j^+3k^) and (i^−j^+k^).
What are the direction cosines of the y-axis?
Find the distance of the point (2i^−j^−4k^) from the plane r⋅(3i^−4j^+12k^)=9.
The direction ratios of a line are 2,6,−9. What are its direction cosines?