A vector $r$ whose magnitude is 12 units and which is equally inclined to the positive axes is

4 \sqrt{3} (i + j + k)

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

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6 \sqrt{2} (i + j)

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6 \sqrt{2} (i + j + k)

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Solution

The correct option is A $4 \sqrt{3} (i + j + k)$
Since, the vector is equally inclined to positive axis
$∴$ Direction cosines are equal.
$\Rightarrow l^{2} + m^{2} + n^{2} = 3 l^{2} = 1$
$\Rightarrow l = \pm \frac{1}{\sqrt{3}}$

$r = | r | (l^i + m^j + n^k)$

$= 4 \sqrt{3} (^i +^j +^k)$

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