Algebra of Vectors: Find Difference & Multiply

[Sam Cepeda]

Homework Statement

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Homework Equations

The Attempt at a Solution

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I am not sure if this is the correct way of finding the difference between two vectors. I thought that if "B" was negative then it's direction would change as well as it's angle. If the angle changes then are my calculations wrong (I used original angle)? I was also curious to know if a similar process applies when multiplying two vectors?

Thanks in advance

 

[haruspex]

Your working is correct.

if "B" was negative then it's direction would change as well as it's angle

A change of angle is a change of direction, no?
You can think of $-\vec B$ as a force of "magnitude" -B in the direction of $\vec B$, or as a force of magnitude B swung round through 180 degrees from $\vec B$. But don't mix the two.
Okay, I know magnitudes are always non negative, hence the quotes.