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Q.

The sum of the three vectors shown in figure is zero. Then the magnitude of the vectors $\vec{O B} and \vec{O C}$ are

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a

5, 5 \sqrt{2}

b

5 \sqrt{2}, 5 \sqrt{2}

c

5 \sqrt{2}, 5

d

\frac{5}{\sqrt{2}}, \frac{5}{\sqrt{2}}

answer is B.

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Detailed Solution

Question Image

$O A = - 5 \hat{j}$

$\vec{O B} = 5 \hat{i}$

$\vec{O C} = OC \cos 45 ° \hat{i} + OC \sin 45 ° \hat{j}$

$\frac{C}{\sqrt{2}} \hat{i} + \frac{C}{\sqrt{2}} \hat{j}$

$5 = \frac{OC}{\sqrt{2}} \Rightarrow OC = 5 \sqrt{2}$

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The sum of the three vectors shown in figure is zero. Then the magnitude of the vectors OB→ and OC→ are