For the question attached, how would you find the values of the vectors BA and BC?

Question

I know that first, you would use the rule

vector BA x vector BC= |vector BA| * |vector BC| * cos[x] and then find the values of vectors BA and BC in terms of a, b and c but I'm not sure as to how...

Answer 1

Yes, you want to use the rule $$ \overrightarrow{BA} \cdot \overrightarrow{BC} = \left|\overrightarrow{BA}\right| \left|\overrightarrow{BC}\right| \cos(\angle ABC) $$ When it says “$A$ is the point defined by the position vector $\mathbf{a} = \mathbf{i} + 3\mathbf{j}$,” it means $A$ is the point $(1,3)$. Similarly, you can find the coordinates of $B$ and $C$, and from those the components of $\overrightarrow{BA}$ and $\overrightarrow{BC}$.