A vector of magnitude $7$ units, parallel to the resultant of the vectors $a = 2 i - 3 j - 2 k$ and $b = - i + 2 j + k,$ is :

\frac{7}{\sqrt{3}} (i + j + k)

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7 (i - j - k)

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\frac{7}{\sqrt{3}} (i - j + k)

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\frac{7}{\sqrt{3}} (i - j - k)

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7 (i + j - k)

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Solution

The correct option is B $\frac{7}{\sqrt{3}} (i - j - k)$
$\to a = 2 i - 3 j - 2 k \to b = - i + 2 j + k$
Le the resultant vector be $\to c$
$\to c = (2 i - 3 j - 2 k) + (- i + 2 j + k) \Rightarrow \to c = i - j - k \land c = \frac{i - j - k}{\sqrt{1^{2} + 1^{2} + 1^{2}}} = \frac{i - j - k}{\sqrt{3}}$
Now a vector of magnitude $7$ paralle to $\to c$ is $\frac{7}{\sqrt{3}} (i - j - k)$
So, option D is correct.

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