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Question Number 120258 by bramlexs22 last updated on 30/Oct/20

	Answered by TANMAY PANACEA last updated on 30/Oct/20

	$\vec{p} = p c o s a i + p s i n a j$ $\vec{q} = q c o s b i - q s i n b j$ $\vec{p} . \vec{q} = (p c o s a i + p s i n a j) . (q c o s b i - q s i n b j)$ $p q c o s a c o s b (i . i) - p q c o s a s i n b i . j + p q s i n c o s b j . i - p q s i n a s i n b (j . j)$ $i . i = 1 j . j = 1 i . j = 0 j . i = 0$ $= p q (c o s a c o s b - s i n a s i n b)$ $a g a i n$ $\vec{p} . \vec{q} = p q c o s (a + b)$ $s o$ $p q c o s (a + b) = p a (c o s a c o s b - s i n a s i n b)$ $c o s (a + b) = c o s a c o s b - s i n a s i n b$
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