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).
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)
To find a unit vector in the direction of vector A = (-1, 2, 3), you need to divide each component of vector A by its magnitude.
1. Calculate the magnitude of vector A:
|A| = sqrt((-1)^2 + 2^2 + 3^2)
= sqrt(1 + 4 + 9)
= sqrt(14)
2. Divide each component of vector A by its magnitude:
A unit vector = (-1/sqrt(14), 2/sqrt(14), 3/sqrt(14))
Therefore, a unit vector in the direction of A = (-1, 2, 3) is (-1/sqrt(14), 2/sqrt(14), 3/sqrt(14)).