If |vec{a}|=2 and |vec{b}|=3,find the value o | vedclass

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(A) From the figure,the angle between vectors $\vec{a}$ and $\vec{b}$ is $	heta = 180^{\circ} - 60^{\circ} = 120^{\circ}$.Let $\vec{A} = 3\vec{a}$ an

Vedclass · Accepted Answer

$6$

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(A) From the figure,the angle between vectors $\vec{a}$ and $\vec{b}$ is $	heta = 180^{\circ} - 60^{\circ} = 120^{\circ}$.Let $\vec{A} = 3\vec{a}$ and $\vec{B} = 2\vec{b}$.Then $|\vec{A}| = 3|\vec{a}| = 3(2) = 6$ and $|\vec{B}| = 2|\vec{b}| = 2(3) = 6$.The magnitude of the resultant vector $\vec{R} = \vec{A} + \vec{B}$ is given by:$|\vec{R}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 + 2|\vec{A}||\vec{B}| \cos 	heta}$$|\vec{R}| = \sqrt{6^2 + 6^2 + 2(6)(6) \cos(120^{\circ})}$Since $\cos(120^{\circ}) = -1/2$:$|\vec{R}| = \sqrt{36 + 36 + 72(-1/2)}$$|\vec{R}| = \sqrt{72 - 36} = \sqrt{36} = 6$.

If $|\vec{a}|=2$ and $|\vec{b}|=3$,find the value of $|3 \vec{a}+2 \vec{b}|$ based on the given figure.

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