Ratio for the length of 2 vectors

Question

I know for this question that a) and b) are correct, but c) is not. Not exactly what it means by "the ratio" so I just took the length of both U and V and divided it.

Answer 1

Your first two calculations are correct. However, on the third one, you gave the value of $\frac{\|u\|}{||v||}$ instead of $\frac{\|v\|}{\|u\|}$.

Therefore, it should be:

$\|u\|=\sqrt{(-1)^2+(2)^2+(1)^2}=\sqrt{6}$

$\|v\|=\sqrt{(3)^2+(3)^2+(6)^2}=\sqrt{54}$

Giving you the answer:

$$\frac{\|v\|}{\|u\|}=\sqrt{\frac{54}{6}}=3$$

Which is the reciprocal of the answer you have written.