Two vectors are given by $\vec{A} = \hat{i} + 2 \hat{j} + 2 \hat{k} a n d \vec{B} = 3 \hat{i} + 6 \hat{j} + 2 \hat{k}$ another vector ‘C’ has the same magnitude as $\vec{B}$ but has the same direction $\vec{A}$ then which of the following vectors represents “C”.

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$\frac{7}{9} (\hat{i} + 2 \hat{j} + 2 \hat{k})$

$\frac{7}{3} (\hat{i} + 2 \hat{j} + 2 \hat{k})$

$\frac{7}{9} (\hat{i} - 2 \hat{j} + 2 \hat{k})$

$\frac{7}{3} (\hat{i} - 2 \hat{j} + 2 \hat{k})$

answer is A.

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Detailed Solution

Vector $\vec{C} = \frac{\vec{A}}{A} \times | \vec{B} |$
$\vec{C} = \frac{\hat{i} + 2 \hat{j} + 2 \hat{k}}{\sqrt{{(1)}^{2} + {(2)}^{2} + {(2)}^{2}}} \sqrt{{(3)}^{2} + {(6)}^{2} {(2)}^{2}}$
$\vec{C} = \frac{7}{3} (\hat{i} + 2 \hat{j} + 2 \hat{k})$

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