Find `lambda` such that the scalar product of the vector `vec i + vec j + vec k` with the unit vector parallel to the sum of the vectors `2 vec i + 4 vec j - 5 vec k` and `lambda vec i + 2 vec j + 3 vec k` is equal to 1.

If the angle between the vectors x vec i + vec j - vec k and vec i + x vec j + vec k is equal to pi/3 then x=_______.

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 .

If vec a=i+j,vec b=j+k and vec c=k+i write unit vectors parallel to vec a+vec b-2vec -

Find a unit vector which is perpendicular to each of the vectors 3vec i+2vec j-vec k and 12vec i+5vec j-5vec k

Find vec a unit vector perpendicular to each of the vectors vec a=3i+2j-3k and vec b=i+j-k

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

The scalar product of the vector vec a=hat i+hat j+hat k with a unit vector along the sum of the vectors vec b=2hat i+4hat j-5hat k and vec c=lambdahat i+2hat j+3hat k is equal to 1. Find the value of lambda and hence find the unit vector along vec b+vec r

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 a vector vec r of magnitude 3sqrt(6) is directed along the bisector of the angle between the vectors vec a=7vec i-4vec j-4vec k and vec b=-2vec i-vec j+2vec k, then vec r is equal to

If vec a=i+2j+k,vec b=2i+j and vec c=3i-4j-5k, then find a unit vector perpendicular to both of the vectors (vec a-vec b) and (vec c-vec b)