Question

Find a vector of magnitude 6 which is perpendicular to both the vectors a = 4 i - j+3 k and b = -2 i+j - 2 k

Answer 1

Let vector r be the vector which is perpendicular to vectors a and b then we have,

r = k.(a x b)…where k is a scalar

Thus, we have r is vector of magnitude 6,

So,

We have,

Thus, substituting the values of a₁, a₂, a₃ and b₁, b₂ and b₃, in equation (i) we get

Here, as r is of magnitude 6 thus,

k = 6,

Thus, vector r = ± 2.(-i+2 j+2 k)