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The sum of the three vectors shown in fi...

The sum of the three vectors shown in figure is zero. Find the magnitudes of the vectors `vec(OB) and vec(OC)`.

Text Solution

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Resolve `vec(OC)` into two rectangular components.
`" "OD= OC cos 45^(@) and OE= OC sin 45^(@)`
For zero resultant `OE= OA or OC sin 45^(@) = 10 N`
`rArr OC xx (1)/(sqrt(2)) =10N rArr |vec(OC)|= 10sqrt2 N`
`and OD= OB rArr OC cos 45^(@) = OB rArr 10sqrt2 xx (1)/(sqrt2) = OB rArr OB = 10N`
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