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  4. The projection of the vector hat i - 2 hat j + hat k on the vector 4 hat i - 4 hat j +7 hat k is

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Q. The projection of the vector $\hat {i} - 2 \hat {j} + \hat {k} $ on the vector $4\hat {i} - 4 \hat {j} +7 \hat {k}$ is

VITEEEVITEEE 2011Vector Algebra

Solution:

Let $a = i - 2j + k$ and $b = 4i - 4j + 7k$, then projection of $a$ on $b$ is equal to
$\frac{a.b}{\left|b\right|}=\frac{4+8+7}{\sqrt{16+16+49}}=\frac{19}{9}$