First slide

Scalars and Vectors

Question

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

Moderate

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

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

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