$\"\"$

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

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(a)

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Find the dot product $\"\"$ .

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

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Compare the vectors with general form.

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$\"\"$ and $\"\"$ .

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

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

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

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Where $\"\"$ and $\"\"$ are magnitudes of the vectors

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The magnitude of the vector $\"\"$ is $\"\"$ .

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$\"\"$ and $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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(c)

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

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Therefore, the two vectors are perpendicular.

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$\"\"$

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

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(b) The angle between the two vectors is $\"\"$ .

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(c) The two vectors are perpendicular.