Free Vectors and Advanced Pure Extensions Quiz | A-Level Mathematics Practice

Vectors and Advanced Pure Extensions

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Find the magnitude of the vector \(\mathbf{a}=3\mathbf{i}-4\mathbf{j}+12\mathbf{k}\), and hence write down the unit vector in the direction of \(\mathbf{a}\).

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\(|\mathbf{a}|=19,\ \hat{\mathbf{a}}=\tfrac{1}{19}(3,-4,12)\)
\(|\mathbf{a}|=13,\ \hat{\mathbf{a}}=\tfrac{1}{13}(3,-4,12)\)
\(|\mathbf{a}|=\sqrt{19},\ \hat{\mathbf{a}}=\tfrac{1}{\sqrt{19}}(3,-4,12)\)
\(|\mathbf{a}|=169,\ \hat{\mathbf{a}}=\tfrac{1}{169}(3,-4,12)\)
\(|\mathbf{a}|=11,\ \hat{\mathbf{a}}=\tfrac{1}{11}(3,-4,12)\)

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