First slide

Vectors

Question

The projection of the vector $\vec{A} = \hat{i} - 2 \hat{j} + \hat{k} on the vector \vec{B} = 4 \hat{i} - 4 \hat{j} + 7 \hat{k} is$

Moderate

A

$\frac{19}{9}$
B

$\frac{38}{9}$
C

$\frac{8}{9}$
D

$\frac{4}{9}$

Solution

Here, $\vec{A} = \hat{i} - 2 \hat{j} + \hat{k}$
$\vec{B} = 4 \hat{i} - 4 \hat{j} + 7 \hat{k}$
The projection of $\vec{A} on \vec{B} = Acosθ$
$Acosθ = \frac{ABcosθ}{B} = \frac{\vec{A} . \vec{B}}{B}$
$= \frac{(\hat{i} - 2 \hat{j} + \hat{k}) . (4 \hat{i} - 4 \hat{j} + 7 \hat{k})}{\sqrt{{(4)}^{2} + {(- 4)}^{2} + {(7)}^{2}}}$
$= \frac{4 + 8 + 7}{\sqrt{81}} = \frac{19}{9}$

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