If `vec a`=`2hati-3hatj+5hatk`,`vec b`=`hati+4hatj+2hatk` then find `vec a xx vec b` and unit vector perpendicular to both `vec a` and `vec b`

If two vectors are given as veca = hati - hatj + 2hatk and vecb = hati + 2hatj+hatk , the unit vector perpendicular to both vec a and vec b is

Let vec a=4hati+5hatj-hatk, vecb = hati -4hatj+5hatk and vec c=3hati+hatj-hatk . Find a vector vec d which is perpendicular to both vec c and vec b and vec d.vec a=21

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

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

Given two vectors veca=-hati + 2hatj + 2hatk and vecb =- 2hati + hatj + 2hatk find |vec a xx vec b|

Consider three vectors vecp=hati+hatj+hatk,vecq=2hati+4hatj-hatk and vecr=hati+hatj+3hatk and let vecs be a unit vector, then vecp,vecq and vecr are

If vec c is perpendicular to both vec a and vec b , then prove that it is perpendicular to both vec a+ vec b and vec a - vec b .

If vec(OA)=2hati-hatj+hatk, vec(OB)=hati-3hatj-5hatk and vec(OC)=3hati-3hatj-3hatk then show that CB is perpendicular to AC.

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) .

Let vec a=hati -2 hatj + 3 hatk, vec b = 3 hati + 3 hatj -hat k and vec c=d hati + hatj + (2d-1) hat k ." If " vec c is parallel to the plane of the vectors veca and vec b, " then " 11 d =