The sum of the magnitudes of two vectors $\vec{A}$ and $\vec{B}$ is 8 and magnitude of the resultant is 4. If the resultant vector is perpendicular to any one vector, then the magnitudes of the two vectors $\vec{A}$ and $\vec{B}$ are

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Aicharya · Accepted Answer

$\begin{aligned} 	herefore &|\vec{A}|=5 \ &|\vec{B}|=8-5 \ &=3 \end{aligned}$ $|\vec{A}+\vec{B}|=4$ $|\vec{A}|+|\vec{B}|=8$ abo $\left.\vec{A}ight|^{2}=|\vec{B}|^{2}|\vec{R}|^{2}$ $|\vec{A}|^{2}=(8-|\vec{A}|)^{2}+4^{2}$ $|\vec{A}|^{2}=64+|\vec{A}|^{2}-16|\vec{A}|+16$ $580=16|\vec{A} \mid$ $|\vec{A} \mid = 5$

The sum of the magnitudes of two vectors $\vec{A}$ and $\vec{B}$ is 8 and magnitude of the resultant is 4.…

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