$\"\"$

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If the angle between the two vectors $\"\"$ and $\"\"$ is $\"\"$ , then $\"\"$ .

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The vectors are $\"\"$ and $\"\"$ .

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Apply dot product formula: $\"\"$ .

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$\"\"$ (Substitute : $\"\"$ )

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$\"\"$ (Simplify) $\"\"$

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Apply dot product property: $\"\"$

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$\"\"$

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$\"\"$ (Simplify)

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$\"\"$

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$\"\"$ (Simplify) $\"\"$

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$\"\"$ (Apply formula: $\"\"$ )

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$\"\"$ (Simplify)

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$\"\"$ ( $\"\"$ )

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$\"\"$

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$\"\"$ ( $\"\"$ ) $\"\"$

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The angle $\"\"$ between the vectors is $\"\"$ .