Find magnitude and direction of a vector, A=(6i^-8j^).

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Find magnitude and direction of a vector, $A = (6 \hat{i} - 8 \hat{j})$ .

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20 units and $53 °$

40 units and $53 °$

10 units and $53 °$

30 units and $53 °$

answer is A.

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Detailed Solution

Magnitude of A

|A| or A= $\sqrt{(6)^{2} + (- 8)^{2}}$

$= 10 units$

Vector A can be shown as

$\tan α = \frac{8}{6} = \frac{4}{3}$

$α = \tan^{- 1} (\frac{4}{3}) = 53 °$

Therefore, $A$ is making an angle of $53 °$ from positive x-axis towards negative y-axis.

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