calc question,,

Question

Since A = 2i - 3j, and B = 5i + 7j, find a unit vector parallel to A.

1. 2/5 I - 3/5 j
2. 1/2 i - 1/3 j
3. 2√13/13 i - 3√13/13 j

Answer 1

Magnitude of the vector is √2² + 9²

√13

a unit vector parallel to A has the same magnitude √13

2/√13 i - 3√13j

rationalize the denominator

3) 2√13/13 i - 3√13/13 j

Answer 2

To find a unit vector parallel to a given vector, divide the given vector by its magnitude. (Do you know how to do this?) Perform the operation, and compare to the choices.

A/|A| = [2 / √(2² + 3²)] i + [-3 / √(2² + 3²)] j = (?)i + (?)j