$\"\"$

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If $\"\"$ and $\"\"$ are two non zero vectors, the projection of $\"\"$ onto $\"\"$ is $\"\"$ .

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The projection of $\"\"$ onto $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$ .

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The projection of $\"\"$ onto $\"\"$ is $\"\"$ .

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$\"\"$

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Consider the vector $\"\"$ .

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The decomposition of $\"\"$ into $\"\"$ and $\"\"$ , where $\"\"$ is parallel to $\"\"$ and $\"\"$ is orthogonal to $\"\"$ is $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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Therefore, $\"\"$ .

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$\"\"$ .

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$\"\"$

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The projection of $\"\"$ onto $\"\"$ is $\"\"$ .

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$\"\"$ .