Unit vector parallel to the resultant of vectors A = 4 i - 3 jand… - Vidyadip

MCQ

Unit vector parallel to the resultant of vectors $\vec A = 4\hat i - 3\hat j$and $\vec B = 8\hat i + 8\hat j$ will be

A
$\frac{{24\hat i + 5\hat j}}{{13}}$
✓
$\frac{{12\hat i + 5\hat j}}{{13}}$
C
$\frac{{6\hat i + 5\hat j}}{{13}}$
D
None of these

✓

Answer

Correct option: B.

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

b
(b) Resultant of vectors $\overrightarrow A $ and $\overrightarrow B $

$\overrightarrow R = \overrightarrow A + \overrightarrow B = 4\hat i - 3\hat j + 8\hat i + 8\hat j$$ = 12\hat i + 5\hat j$

$\hat R = \frac{{\overrightarrow R }}{{|R|}} = \frac{{12\hat i + 5\hat j}}{{\sqrt {{{(12)}^2} + {{(5)}^2}} }}$$ = \frac{{12\hat i + 5\hat j}}{{13}}$

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