1. ## Angle at Ox

I'm really confused on which angle here is "the angle at Ox", and how you find out.

That's a quick image I made of it. I have that as the vector $|-3i + 2j|$ but I'm not sure whether the angle is $a$ or $a + b$ or $b + c$ or $a + b + c$.

2. Originally Posted by Viral
That's a quick image I made of it. I have that as the vector $|-3i + 2j|$ but I'm not sure whether the angle is $a$ or $a + b$ or $b + c$ or $a + b + c$.
From your graphic, the usual understanding of $O_x=b+c$.
The that angle is $\pi + \arctan \left( {\frac{2}{{ - 3}}} \right)$.

However, you need to check your text material for the wanted definition.

3. That's the problem =\ , the only information given is:

Given that $a = i + j$ and $b = 2i - j$ find the magnitude of each of the following vectors and the angle each makes with Ox.
So, for the above example, it's the same as $180 - arctan(\frac{2}{3})$ ?

What about with this example: ?

I've been answering those ones as just $\theta = arctan(\frac{j}{i})$

EDIT: The a and b referred to in the information given is not referring to the angles, I should have given them different variables...

4. It appears to me as if your text material is not standard.
So you really need to read it closely to find these definitions.

I can give a standard approach. Consider the vector $p\vec{i}+q\vec{j}$.
The angle associated with that vector is: $\left\{ {\begin{array}{rl} {\arctan \left( {\frac{q}{p}} \right),} & {p > 0} \\ {\pi + \arctan \left( {\frac{q}{p}} \right),} & {p < 0\;\& \;q > 0} \\ { - \pi + \arctan \left( {\frac{q}{p}} \right),} & {p < 0\;\& \;q < 0} \\ \end{array} } \right.$