The sum of three vectors is zero as shown in | vedclass

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(A) Given that the sum of the three vectors is zero,i.e.,$\vec{OA} + \vec{OB} + \vec{OC} = 0$.From the figure,$\vec{OA}$ is acting downwards with a ma

Vedclass · Accepted Answer

$10 \, N, \, 10 \sqrt{2} \, N$

Vedclass · Answer

(A) Given that the sum of the three vectors is zero,i.e.,$\vec{OA} + \vec{OB} + \vec{OC} = 0$.From the figure,$\vec{OA}$ is acting downwards with a magnitude of $10 \, N$.To balance the vertical component of $\vec{OC}$,the vertical component of $\vec{OC}$ must be equal to the magnitude of $\vec{OA}$.Let $	heta = 45^\circ$ be the angle $\vec{OC}$ makes with the horizontal axis $OD$.The vertical component of $\vec{OC}$ is $OC \sin(45^\circ) = OA = 10 \, N$.Therefore,$OC = \frac{10}{\sin(45^\circ)} = \frac{10}{1/\sqrt{2}} = 10\sqrt{2} \, N$.The horizontal component of $\vec{OC}$ is $OC \cos(45^\circ) = (10\sqrt{2}) 	imes (1/\sqrt{2}) = 10 \, N$.Since the sum of vectors is zero,the horizontal component of $\vec{OC}$ must be balanced by $\vec{OB}$.Thus,$OB = 10 \, N$.So,the magnitudes are $OB = 10 \, N$ and $OC = 10\sqrt{2} \, N$.

The sum of three vectors is zero as shown in the figure. What will be the magnitudes of vectors $\vec{OB}$ and $\vec{OC}$?

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