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**shenanigans87** Let a be a unit vector and let |b| = 4. Let the angle between these two vectors be 30 degrees. Calculate (2a - b) DOT (5a + 3b).

If **a** is a unit vector, let it equal {1,0,0}

then by taking the sin and cos of 30, we know that **b** would be $\displaystyle (\frac{\sqrt{3}}{2},\frac{1}{2},0)$

but since |b|=4, **b** is really equal to

$\displaystyle 4*(\frac{\sqrt{3}}{2},\frac{1}{2},0)=(2\sqrt{3},2, 0)$

now that you know **a** and **b**, you should be able to do those dot products pretty easily.