| Six vectors \[\overset{\to }{\mathop{\mathbf{a}}}\,\] through \[\overset{\to }{\mathop{\mathbf{f}}}\,\] have the magnitudes and directions indicated in the figure. Which of the following statements is true? [AIPMT (S) 2010] |
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A) \[\overset{\to }{\mathop{\mathbf{b}}}\,\,+\overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{f}}}\,\]
B) \[\overset{\to }{\mathop{\mathbf{d}}}\,\,+\overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{f}}}\,\]
C) \[\overset{\to }{\mathop{\mathbf{d}}}\,\,+\overset{\to }{\mathop{\mathbf{e}}}\,=\overset{\to }{\mathop{\mathbf{f}}}\,\]
D) \[\overset{\to }{\mathop{\mathbf{b}}}\,\,+\overset{\to }{\mathop{\mathbf{e}}}\,=\overset{\to }{\mathop{\mathbf{f}}}\,\]
Correct Answer: C
Solution :
If two non-zero vectors are represented by the two adjacent sides of a parallelogram, then the resultant is given by the diagonal of the parallelogram passing through the point of intersection of the two-vectors \[\therefore \] \[\overset{\to }{\mathop{\mathbf{d}}}\,+\overset{\to }{\mathop{\mathbf{e}}}\,=\overset{\to }{\mathop{\mathbf{f}}}\,\]
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