If `vec(OP)=2hati+3hatj-hatk and vec(OQ)=5hati+4hatj-3hatk`. Find `vec(PQ)` and the direction cosines of `vec(PQ)`.

If vec(OP)=2hati+3hatj-hatk and vec(OQ)=3hati-4hatj+2hatk find the modulus and direction cosines of vec(PQ) .

(i) Find the unit vector in the direction of veca+vecb if veca=2hati-hatj+2hatk , and vecb=-hati+hatj-hatk (ii) Find the direction ratios and direction cosines of the vector veca=5hati+3hatj-4hatk .

The position vectors of A and B are 3hati - hatj +7hatk and 4hati-3hatj-hatk . Find the magnitude and direction cosines of vec(AB) .

If vecF = 3hati + 4hatj+5hatk and vecS=6hati +2hatj+5hatk , the find the work done.

If in parallelogram ABCD, diagonal vectors are vec(AC)=2hati+3hatj+4hatk and vec(BD)=-6hati+7hatj-2hatk , then find the adjacent side vectors vec(AB) and vec(AD) .

If vec a = hati + 2 hatj + 2 hat k and vec b = 3 hati + 6 hatj + 2 hat k then the vector in the direction of vec a and having mgnitude as |vec b| is

If vec(OA) =2hati+3hatj-4hatk and vec(OB) =hatj+hatk are two vectors through the origin O, find the projection of vec(OA) and vec(OB)

If vec(OA) =2hati+3hatj-4hatk and vec(OB) =hatj+hatk are two vectors through the origin O, find the projection of vec(OB) on vec(OA) .

The position vectors of two points A and B are hati+hatj+hatk and 5hati-3hatj+hatk . Find a unit vector in direction of vec(AB) , and also find the direction cosines of vec(AB) . What angles does vec(AB) make with the three axes?

If vecF=3hati-4hatj+5hatk " and " vecS=6hati+2hatj+5hatk , the find the work done.