Unit vector parallel to resultant of vectors vec A = 4hat{i} - 3hat{j} and vec B = 8hat{i} + 8hat{j}

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3-1.Vectors

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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

$\frac{{24\hat i + 5\hat j}}{{13}}$

B

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

C

$\frac{{6\hat i + 5\hat j}}{{13}}$

D

None of these

Solution

(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}}$

Standard 11

Physics

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