$\"\"$

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

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(a)

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Find the projection of u onto v.

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Definition of Projection using the dot product :

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

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$\"\"$

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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

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$\"\"$

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(b)

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Find the vector component of u orthogonal to v.

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Definition of vector component :

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The vector component of u orthogonal to v is $\"\"$ .

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Where $\"\"$ is the projection of u onto v.

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$\"\"$

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The vector component of u orthogonal to v is $\"\"$ .

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$\"\"$

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(a) The projection of u onto v is $\"\"$ .

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(b) The vector component of u orthogonal to v is $\"\"$ .