$\"\"$

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

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(a) Find the dot product $\"\"$ .

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Dot product definition: $\"\"$ .

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$\"\"$

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$\"\"$ .

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The dot product of the two vectors is $\"\"$ .

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$\"\"$

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(b) Find the angle between $\"\"$ and $\"\"$ .

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Cosine of the angle between two vectors: $\"\"$ .

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Find magnitude of vector $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Find magnitude of vector $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Apply formula: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"italic$

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$\"italic$ .

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$\"\"$

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(c)

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Dot product of the vectors $\"\"$ , so the vectors are orthogonal.

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The vectors are orthogonal.

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$\"\"$

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(a) $\"\"$ .

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(b) The angle $\"italic$ .

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(c) The vectors are orthogonal.