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))`.

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

If veca = 3hati - hatj - 4hatk , vecb = -2hati + 4hatj - 3hatk and vec c = hati + 2hatj - hatk then |3veca - 2vec b + 4vec c | is equal to

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

If veca = 5 hati- 4 hatj + hatk, vecb =- 4 hati + 3 hatj - 2 hatkand vec c = hati - 2 hatj - 2 hatk, then evaluate vec c. (veca xx vecb)

Consider the equations of the straight lines given by : L_(1) : vec(r) = (hati + 2 hatj + hatk ) + lambda ( hati - hatj + hatk) L_(2) : vec(r) = (2 hati - hatj - hatk) + mu ( 2 hati + hatj + 2 hatk) . If vec(a_(1))= hati + 2 hatj + hatk, " " vec(b_(1)) = hati - hatj + hatk , vec(a_(2)) = 2 hat(i) - hatj - hatk, vec(b_(2)) = 2 hati + hatj + 2 hatk , then find : (i) vec(a_(2)) - vec(a_(1)) " " (ii) vec(b_(2)) - vec(b_(1)) (iii) vec(b_(1))xx vec(b_(2)) " " (iv) vec(a_(1)) xx vec(a_(2)) (v) (vec(b_(1)) xx vec(b_(2))).(vec(a_(1)) xxvec(a_(2))) (vi) the shortest distance between L_(1) and L_(2) .

If veca=x hati+y hatj+z hatk, vecb=y hati+z hatj+x hatk, and vec c=z hati+x hatj+y hatk , then veca xx (vecb xx vec c) is :

If vec r = 3 hati + 2 hatj - 5 hatk , vec a= 2 hati - hatj + hatk, vec b = hati + 3 hatj - 2hatk and vec c=2 hati + hatj - 3 hatk " such that " hat r = x vec a +y vec b + z vec c then

If veca = hati - hatj + hatk, vecb= 2 hati + hatj -hatk and vec c = lamda hati -hatj+ lamda hatk are coplanar, find the value of lamda.

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))

Find the angle between the vertors vec(A) = hati + 2hatj - hatk and vec(B) = - hati +hatj - 2hatk .