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The projection of the vector $\boldsymbol{i}-2 \boldsymbol{j}+\boldsymbol{k}$ on the vector $4 i-4 j+7 k$ is
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Verified Answer
The correct answer is:
$\frac{19}{9}$
Let $\mathbf{a}=\mathbf{i}-2 \mathbf{j}+\mathbf{k}$ and $\mathbf{b}=4 \mathbf{i}-4 \mathbf{j}+7 \mathbf{k}$, then projection of $\mathbf{a}$ on $\mathbf{b}$ is equal to
$$
\frac{\text { a.b }}{|\mathbf{b}|}=\frac{4+8+7}{\sqrt{16+16+49}}=\frac{19}{9}
$$
$$
\frac{\text { a.b }}{|\mathbf{b}|}=\frac{4+8+7}{\sqrt{16+16+49}}=\frac{19}{9}
$$
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