If the volume of a parallelopiped, whose three coterminous edges are `-12 vec i + lambda vec k; `
` 3 vec j - vec k` and `2 vec i + vec j - 15 vec k`, is 546 then `lambda`=_______.

| 2vec i-3vec j + vec k | =

(vec i + xvec j + 3vec k) xx (vec i-vec j + vec k) = 5vec i + xvec j-3vec k then x =

Find the value of: (vec j xxvec k) * (3vec i + 2vec j-vec k)

Find the unit vector in the direction of the vector vec a + vec b if vec a =vec i +2 vec j + 3 vec k and vec b = 2 vec i + 3 vec j + 5 vec k .

The sine of the angle between the vectors vec i+3vec j+2vec k and 2vec i-4vec j+vec k is

Find the volume of the parallelopiped whose edges are represented by veca=vec(2i)-vec(3j)+vec4k, vecb=veci+vec(2j)-veck and vecc=vec(3i)-vecj+vec(2k)

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors: vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j+2 hat k vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j-2 hat k vec a=11 hat i , vec b=2 hat j- hat k , vec c=13 hat k vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k

Prove that the vectors 3 vec I + 5 vec j + 2 vec k, 2 vec I - 3 vec j - 5 vec k and 5 vec I + 2 vec j -3 vec k form the sides of an equilatera, triangle.

If the area of the parallelogram whose adjacent sides are 3vec i-4vec j+lambdavec k and 2vec j-4vec k is sqrt(436) sq units then find the value of lambda

If | vec a | = 2, | vec b | = 7 and vec a xxvec b = 3vec i + 2vec j + 6vec k then vec a * vec b =