As shown in the above diagram , the inner product of the 2 vectors is given as the formula below.
$$ \boldsymbol{H}\cdot\boldsymbol{M} = \left\{ H_{r}M \cos\left(\phi_{} \right) + H_{\theta_{} }M \sin\left(\phi_{} \right) \right\} \tag{1} $$
Why this equation can be obtained? Why cosine and sine appeared?
I know the below definitions of a inner product.
$$ \boldsymbol{a}= \left( x_{1},x_{2},x_{3} \right) ~~,~~ \boldsymbol{b}= \left( y_{1},y_{2},y_{3} \right) ~$$
$$~ \boldsymbol{a}\cdot\boldsymbol{b} = \prod_{ i=1 }^{ 3 } x_{i}y_{i} = \left| \left| a \right| \right| \cdot \left| \left| b \right| \right| \cos\left(\text{angle between the vectors} \right) $$
Can I still deduce the equation1 from the above definitons?
Or even a misprint?