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Vector $\vec{A}$ which is directed along x-axis, is to be added to vector $\vec{B},$ which has a magnitude of 7.0m. The sum is a third vector that is directed along the Y-axis with magnitude that is 3 times that of A. The magnitude of $\vec{A}$ is $\frac{7}{\sqrt{x}};$ value of x is ____.

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answer is 10.

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Detailed Solution

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$| \vec{C} | = 3 | \vec{A} |$
$| \vec{B} | = \sqrt{{| \vec{C} |}^{2} + {| \vec{A} |}^{2}} = \sqrt{{(3 | \vec{A} |)}^{2} + {| \vec{A} |}^{2}} = \sqrt{10} A \Rightarrow A = \frac{B}{\sqrt{10}} = \frac{7}{\sqrt{10}}$

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