Question

Unit vector parallel to the resultant of vectors $\overrightarrow{A} = 4\widehat{i} - 3\widehat{j}$and $\overrightarrow{B} = 8\widehat{i} + 8\widehat{j}$will be

• A. $\frac{24\widehat{i} + 5\widehat{j}}{13}$
• B. $\frac{12\widehat{i} + 5\widehat{j}}{13}$
• C. $\frac{6\widehat{i} + 5\widehat{j}}{13}$
• D. None of these

Answer 1

Answer: (B)

$\frac{12\widehat{i} + 5\widehat{j}}{13}$

Answer 2

Resultant of vectors $\overset{\rightarrow}{A}$ and $\overset{\rightarrow}{B}$

$\overset{\rightarrow}{R} = \overset{\rightarrow}{A} + \overset{\rightarrow}{B} = 4\widehat{i} - 3\widehat{j} + 8\widehat{i} + 8\widehat{j}$ $= 12\widehat{i} + 5\widehat{j}$

$\widehat{R} = \frac{\overset{\rightarrow}{R}}{|R|} = \frac{12\widehat{i} + 5\widehat{j}}{\sqrt{(12)^{2} + (5)^{2}}} = \frac{12\widehat{i} + 5\widehat{j}}{13}$