Answer:
See below for answers and explanations
Step-by-step explanation:
<u>Problem 1</u>
Rewrite and add each vector:

Find the magnitude of the resulting vector:

Therefore, the best answer is D) 64.959
<u>Problem 2</u>
Think of the vectors like this:

By adding the vectors, we have:

Since the direction of a vector is
, we have:

Don't forget to take into account that the resulting vector is in Quadrant IV since the horizontal component is positive and the vertical component is negative, so we will add 360° to our angle to get the result:

Therefore, the best answer is D) 320°
<u>Problem 3</u>
Again, rewrite the vectors and add them:

Using the direction formula:

As the vector is located in Quadrant II, we need to add 180° to our angle:

Therefore, the best answer is D) 173°
<u>Problem 4</u>
Using scalar multiplication:

Find the magnitude of the resulting vector:

Find the direction of the resulting vector:

As the vector is located in Quadrant II, we need to add 180° to our angle:

Therefore, the best answer is C) 111; 161°
<u>Problem 5</u>
Using scalar multiplication:

Since the direction of the angle doesn't change in scalar multiplication, it only affects the magnitude, so the magnitude of the resulting vector would be
, making the correct answer C) 125; 200°