Given three vectors A = (1, 1, 1), B = (-1, 2, 3) and C = (0, 3, 4), find the unit vector in the direction of A+B – C.

Answer 1

To find the unit vector in the direction of A + B - C, we need to first find the vector A + B - C and then normalize it.

Adding the three vectors, we get:

A + B - C = (1, 1, 1) + (-1, 2, 3) - (0, 3, 4)
= (1, 1, 1) - (1, 2, 3)
= (1 - 1, 1 - 2, 1 - 3)
= (0, -1, -2)

To normalize this vector, we divide each component by its magnitude:

Magnitude of (0, -1, -2) = sqrt(0^2 + (-1)^2 + (-2)^2) = sqrt(0 + 1 + 4) = sqrt(5)

So, the unit vector in the direction of A + B - C is:

(0, -1, -2) / sqrt(5)