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(B) Let the initial vector be $\vec{A} = 4\hat{i} + 10\hat{j}$.The magnitude of the vector is $|\vec{A}| = \sqrt{(4)^2 + (10)^2} = \sqrt{16 + 100} = \

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$7.2$

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(B) Let the initial vector be $\vec{A} = 4\hat{i} + 10\hat{j}$.The magnitude of the vector is $|\vec{A}| = \sqrt{(4)^2 + (10)^2} = \sqrt{16 + 100} = \sqrt{116} ~m$.When the vector is rotated, its magnitude remains constant.Let the new vector be $\vec{A}' = 8\hat{i} + n\hat{j}$, where the $x$-component is doubled $(4 	imes 2 = 8)$.Since the magnitude is conserved, $|\vec{A}'| = |\vec{A}|$.Therefore, $\sqrt{(8)^2 + n^2} = \sqrt{116}$.Squaring both sides, we get $64 + n^2 = 116$.$n^2 = 116 - 64 = 52$.$n = \sqrt{52} \approx 7.21 ~m$.Thus, the new $y$-component is approximately $7.2 ~m$.

$A$ certain vector in the $xy$-plane has an $x$-component of $4 ~m$ and a $y$-component of $10 ~m$. It is then rotated in the $xy$-plane so that its $x$-component is doubled. Then its new $y$-component is (approximately) (in $~m$)

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