The vectors i (1, 0, 0), j = (0, 1, 0) and k = (0, 0, 1) are unit vectors in the direction of positive x, y and z axis, respectively. Find a unit vector in the direction of A = (-1, 2, 3).

Answer 1

To find a unit vector in the direction of A = (-1, 2, 3), we need to divide A by its magnitude.

The magnitude of A is given by:

|A| = √((-1)^2 + 2^2 + 3^2)
= √(1 + 4 + 9)
= √14

Therefore, a unit vector in the direction of A is given by:

 = A/|A|
= (-1/√14, 2/√14, 3/√14)