Find a vector whose magnitude is 3 units and which is perpendicular to each of the vectors a=3i+j-4k and b=6i+5j-2k

Question

Vector algebra

Class 12 CBSE

Answer 1

Let our vector C = xi + yj + zk.

So we have equations: 3x + y - 4z = 0 and 6x + 5y - 2z = 0

or 3x + y = 4z and 6x + 5y = 2z

If we multiply 1st equation by - 2 and add we get 3y = - 6z, y = - 2z, x = 2z.

So, vector C = 2zi - 2zj + zk; Now (2z)² + (-2z)² + z² = 3². 9z² = 9, z² = 1, z = ± 1

We get 2 vectors : C = 2i - 2j + k or C = -2i + 2j - k