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

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

If vec(A) = hati + 3hatj + 2hatk and vec(B) = 3hati + hatj + 2hatk , then find the vector product vec(A) xx vec(B) .

If vec(A) = 2hati +3 hatj +hatk and vec(B) = 3hati + 2hatj + 4hatk , then find the value of (vec(A) +vec(B)) xx (vec(A) - vec(B))

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) = 3 hati +2hatj and vec(B) = hati - 2hatj +3hatk , find the magnitudes of vec(A) +vec(B) and vec(A) - vec(B) .

Let vec(a)=2hati-hatj+hatk,vec(b)=hati+2hatj-hatk and vec( c )=hati+hatj-2hatk be three vectors. A vector in the plane of vec(b) and vec( c ) whose projection on vec(a) is of magnitude sqrt(2//3) is

Two vectors vec P and vec Q are given by vec P =3 hati + 4hatj+5hat k vec Q =2hati +2 hatj+3hatk What are the direction cosines of the vector (vec P - vec Q) ?

Let O be the origin. Let vec(OP) = x hati+y hati-hatk and vec(OQ) = -hati+2hatj+3x hatk, x y in R , x gt 0 , be such that |vec(PQ)|=sqrt(20) and the vector vec(OP) is perpendicular to vec(OQ) . If vec(OR)=3hati+zhatj-7hatk, z in R , is coplanar with vec(OP) and vec(OQ) , then the value of x^(2)+y^(2)+z^(2) is equal to :

If vec A=hati +7hatj +hatk and vec B =2 hati+3hatj +4hatk then the component of vec A along vec B is

If vec(a) = hati - 2hatj - 3hatk, vec(b) = 2hati +hatj - hatk and vec(c) = hati +3hatj - 2hatk then find vec(a) xx (vec(b) xx vec(c)) .