The sum of three vectors shown in Fig. 2 ( c) . 77. is zero .
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(a) What is the magnitude of the vector ` vec (OB) ?
(b) What is the magnitude of the vector ` vec (OC)` ?

Explanation

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Resolving ` vec (OC)` into two rectangular components, we have ` OC cos 45^@` aling ` OD` and (OC sin 45^@` along ` OE` . Since the sum of the three vectors is zero , so the particle in equilibrium under the effect of applied forces.
Hence, ` OB=OC cos 45^@` ...(i) ltBRgt and ` OA =OC sin 45^@` ltbRgt or ` OC = (OA)/( sin 45^@) = 5/( 1 //sqrt 2) = 5 sqrt 2 m` ltbRgt From (i), ` OB= OC cos 45^2 = 5 sqrt 2 xx 1/( sqrt 2) = 5 sm`.