Let $| \mathbf { a } | = 1$ And $| \mathbf { b } | = 2$

Essay

Let $| \mathbf { a } | = 1$ and $| \mathbf { b } | = 2$ and the angle between a and b be 150°. Find
(i) $\mathbf { a } \cdot \mathbf { b }$ (ii) $\mathbf { b } \cdot ( 3 \mathbf { a } + \mathbf { b } )$ (iii) $( \mathbf { a } + \mathbf { b } ) \cdot ( \mathbf { a } - \mathbf { b } )$ (iv) $| 2 a - b | ^ { 2 }$