If the vectors `vec a + vec b + vec c, vec a + lambda vec b + 2 vec c, - vec a + vec b + vec c` are linearly dependent then `lambda`

If vec a , vec b and vec c are non-coplanar (independent) vectors, prove that the vectors vec a- 2 vec b+ 3 vec c , -2 vec a + 3 vec b- 4 vec c and vec a -vec b+ 2 vec c are also linearly independent.

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

Let vec a, vec b, vec c be three nonzero vectors such that vec a + vec b + vec c = vec 0 and lambdavec b xxvec a + vec b xxvec c + vec c xxvec a = 0 then lambda is

If the lines vec r = vec a + lambda (vec b xx vec c) and vec r = vec b + mu (vec c xx vec a) are intersect then ...............

Let lambda = vec a xx (vec b + vec c), vec mu = vec b xx (vec c + vec a) and vec nu = vec c xx (vec a + vec b). Then

Let vec a , vec b and vec c be three non-zero vectors such that vec a+ vec b+ vec c=0 and lambda vec bxx vec a+ vec bxx vec c+ vec cxx vec a=0, then find the value of lambda

Let vec a , vec b and vec c be three non-zero vectors such that vec a+ vec b+ vec c=0 and lambda vec bxx vec a+ vec bxx vec c+ vec cxx vec a=0, then find the value of lambda

For any three vectors vec a, vec b , vec c , show that vec a xx (vec b + vec c) + vec b xx (vec c + vec a) + vec c xx (vec a + vec b) = 0

If [3 vec a+7 vec b\ vec c\ vec d]=lambda[ vec a\ vec c\ vec d]+mu[ vec b\ vec c\ vec d] , then find the value of lambda+mudot

If vec a, vec b, vec c are three vectors such that vec a . (vec b + vec c) + vec b . (vec c + vec a) + vec c . (vec a + vec b) = 0 and |vec a| = 1, |vec b | = 4, |vec c| = 8 , then |vec a + vec b + vec c| =