Question

solve the following question
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Answer 1

QUESTION:

Six vectors, $\vec{a}$ through $\vec{f}$ have the magnitudes and directions indicated in the figure. Which of the following statements is true?

ANSWER:

• Option c) $\vec{d}+\vec{e}=\vec{f}$

TO FIND:

• The true statement.

EXPLANATION:

A) (REFER ATTACHMENT 1)

$Here \ \vec{c} , \ \vec{b} \ and \ \vec{f} \ are \ in \ head \ to \ tail \ manner.$

$\therefore \vec{b} + \vec{c} + \vec{f}=0$

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

Option A) is incorrect.

B) (REFER ATTACHMENT 2)

$Here \ \vec{c} \ and \ \vec{f} \ are \ in \ same\ manner.$

$\vec{d} \ is \ in\ opposite \ manner.$

$\therefore \vec{c} + \vec{f} = \vec{d}$

$\vec{f} = \vec{d} - \vec{c}$

Option B) is incorrect.

C) (REFER ATTACHMENT 3)

$Here \ \vec{d} \ and \ \vec{e} \ are \ in \ same\ manner.$

$\vec{f} \ is \ in \ opposite \ manner.$

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

Option C) is correct.

D) (REFER ATTACHMENT 4)

$Here \ \vec{e} \ and \ \vec{f} \ are \ in \ same\ manner.$

$\vec{b} \ is \ in\ opposite \ manner.$

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

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

Option D) is incorrect.