Do you know anything about vectors in geometry?

Find the magnitude of the vector (6,-3) to the nearest tenth.


a. 6.7 c. 45.0


b. 5.2 d. 9.0











A current’s velocity is given by the vector (3,1) . Find the direction of the vector to the nearest tenth of a degree.


a. 18.4 c. 30.0


b. 71.6 d. 19.5








PLEASE EXPLAIN YOUR ANSWER!? Thanks You! ♥

Do you know anything about vectors in geometry?
Okay.


The first question. The magnitude of a vector is determined by the square root of a^2 + b^2, so in this vector, it's the square root of 6^2 + -3^2, which equals the square root of 36 + 9, which equals the square root of 45. That's about equal to 6.7 so the answer is a.





For the second question. The direction of a vector is determined by the inverse tangent of b over a. So it's the inverse tangent of 1/3, which according to my calculator should be 18.4, so your answer is a.





Hope this helps!