Question

The unit vector parallel to the resultant of the vectors

$\overset{\rightarrow}{A} = 4\widehat{i} + 3\widehat{j} + 6\widehat{k}$and$\overset{\rightarrow}{B} = - \widehat{i} + 3\widehat{j} - 8\widehat{k}$ is –

• A. (a)$\frac{1}{7}(3\widehat{i} + 6\widehat{j} - 2\widehat{k})$
• A. (b)$\frac{1}{7}(3\widehat{i} + 6\widehat{j} + 2\widehat{k})$
• A. (c)$\frac{1}{49}(3\widehat{i} + 6\widehat{j} + 2\widehat{k})$
• A. (d)$\frac{1}{49}(3\widehat{i} + 6\widehat{j} - 2\widehat{k})$

Answer 1

(a)

$\overset{\rightarrow}{C} = \overset{\rightarrow}{A} + \overset{\rightarrow}{B}$ = $(3\widehat{i} + 6\widehat{j} - 2\widehat{k})$

$\widehat{C} = \frac{\overset{\rightarrow}{C}}{|C|}$ = $\frac{3\widehat{i} + 6\widehat{j} - 2\widehat{k}}{\sqrt{3^{2} + 6^{2} + (–2)^{2}}}$ = $\frac{3\widehat{i} + 6\widehat{j} - 2\widehat{k}}{7}$