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Vector Addition

Six vectors, ...

Question

Six vectors, $\to a$ to $\to f$ , all of magnitude 1 and directions indicated in the figure ( Consider all of them to be originating at origin ). Which of the following statement is true?

\to b + \to e = \to f

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\to b + \to c = \to f

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\to d + \to c = \to f

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\to d + \to e = \to f

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Solution

The correct option is C $\to d + \to e = \to f$
We have, assuming unit magnitude for all vectors:
$\to a = \to i$
$\to b = - \to - j$
$\to c = \to i$
$\to d = \to j$
$\to e = - \to - i$
$\to f = - \to - i + \to j$
$∴ \to d + \to e = \to j + - \to - i$

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