Let `vecF=2hati+4hatj+3hatk` at the point P with position vector `hati-hatj+3hatk`. Find the moment of `vecF` about the line through the origin O in the direction of the vector `veca=hati+2hatj+2hatk`.

For given vectors, veca=2hati-hatj+2hatk and vecb=-hati+hatj-hatk , find the unit vector in the direction of the vector veca + vecb

A line passing through the point A with position vector veca=4hati+2hatj+2hatk is parllel to the vector vecb=2hati+3hatj+6hatk .Find the length of the perpendicular drawn on this line from a point P with position vector vecr_1=hati+2hatj+3hatk .

Find the unit vector in the direction of the sum of the vectors, veca = 2hati+2hatj-5hatk and vecb=2hati+hatj+3hatk .

Find the vector equation of a line passing through the point with position vector hati-2hatj-3hatk and parallel to the line joining the points with position vectors hati-hatj+4hatk and 2hati+hatj+2hatk . Also find the cartesian form of the equation.

Show that the three points with position vectors -2hati+3hatj+5hatk , hati+2hatj+3hatk and 7hati-hatk are collinear.

Find the vector equation of a line passing through a point with position vector 2hati-hatj+hatk and parallel t the line joining the points with position vectors -hati+4hatj+hatk and hati+2hatj+2hatk . Also, find the cartesian equivalent of the equation.

Find the vector projection of the vector 7hati+hatj-hatk on : 2hati+6hatj+3hatk .