First slide

Vectors

Question

If $A = 4 \hat{i} - 3 \hat{j} and B = 6 \hat{i} + 8 \hat{j}$ then magnitude and direction of A + B with X-axis will be

Moderate

A

5, tan^-1 (3/4)
B

$5 \sqrt{5}, \tan^{- 1} (1 / 2)$
C

10, tan^-1 (5)
D

25, tan^-1 (3/4)

Solution

$A + B = 10 \hat{i} + 5 \hat{j}$
$∴$ $| A + B | = \sqrt{100 + 25} = 5 \sqrt{5}$
Angle of A + B with X-axis
$θ = \tan^{- 1} (\frac{5}{10}) = \tan^{- 1} (\frac{1}{2})$

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