Six vectors $\vec{a}, \vec{b}, \vec{c}, \vec{d}, \vec{e} a n d \vec{f}$ having magnitudes and direction on indicated in the figure. Which of the following state is true?

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$\vec{d} + \vec{e} = \vec{f}$

$\vec{b} + \vec{c} = \vec{f}$

$\vec{d} + \vec{b} = \vec{f}$

$\vec{b} + \vec{e} = \vec{f}$

answer is D.

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Detailed Solution

Consider the problem
The $\vec{f}$ vector has the resultant of any two other vector.
By parallelogram law of vector addition.
Let $\vec{f}$ be the resultant between $\vec{d} a n d \vec{e}$
Therefore, $\vec{d} + \vec{e} = \vec{f}$

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