The unit vector which is orthogonal to the vector `3 vec i +2 vec j + 6 vec k` and is coplanar with the vector `2i+j+k` and `i -j+k`

The unit vector which is orthogonal to the vector vec a = 3i+2j+6k and is coplanar with the vectors vec b = 2i+j+k and vec c = i-j+k is

The unit vector which is orthogonal to the vector 5i+2j+6k and is coplanar with the vectors 2i+j+k" and "i-j+k is

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 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 .

What is the unit vector hat a parallel to the vector vec a= 3 vec I + 4 vec j - 2 vec k ? Find the vector vec b such that hat a + vec b becomes the unit vector vec i ?

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.

Vector of length of 3 unit which is perpendicular to vec i + vec j + vec k and lies in the plane of vec i + vec j + vec k and 2vec i-3vec j, is (1) (3) / (sqrt ( 6)) (vec i-2vec j + vec k) (2) (3) / (sqrt (6)) (2vec i-vec j-vec k) (3) (3) / (sqrt (114)) ( 8vec i-7vec j-vec k) (4) (3) / (sqrt (114)) (- 7vec i + 8vec j-vec k)

The projection of vec a = 3i +2k on the vector vec b = 2i + 3j +k is,

If vec(a)=hat(i)+hat(j)-4hat(k) " and " vec(b)=4hat(i)-hat(j)-2hat(k) , then find (i) a unit vector in the direction of the vector (2vec(a)-vec(b)) and (ii) vector and scalar components of the vector (2vec(a)-vec(b)) along coordinate axes.