Find the cosine angles between the vectors $2 ¯ i + 2 ¯ j - ¯ ¯ ¯ k$ and $6 ¯ i - 3 ¯ j + 2 ¯ ¯ ¯ k$

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Solution

If two vectors $\to a$ and $\to b$ is given, then cosine angle between them is given as $c o s θ = \frac{\to a . \to b}{| | a | | | | b | |}$
Here $| | a | | = \sqrt{4 + 4 + 1}$ and $| | b | | = \sqrt{36 + 9 + 4}$
$\to a . \to b = 12 - 6 - 2 = 4$
$c o s θ = \frac{4}{3 \times 7} = \frac{4}{21}$

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