Find the components of a vector `vecA` along two direction making angles `alpha and beta` respectively with the vector.

Find the angle between two vectors vecaandvecb with magnitudes 1 and 2 respectively and when veca*vecb=1 .

If vec alpha, vec beta, vecgamma be three unit vectors such that |vec alpha+vec beta+vec gamma|=1 and vec alpha is perpendicular to vec beta while vec gamma makes angles theta and phi with vec alpha and vec beta respectively, then the value of cos theta+cos phi is -

Find the angle between two vectors vecaandvecb with magnitudes sqrt(3)and2 , respectively having veca*vecb=sqrt(6) .

Find the direction cosines for the vector veca=4hati+6hatj-5hatk .

Show that the projection or component of a vector vecR on another vector vecA is vecR*hata , where hata is a unit vector along vecA .