Let $\to A$ and $\to B$ be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angles $30^{0}$ and $60^{0}$ respectively, find the resultant.

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Solution

Angle between the vectors $θ = 60^{0} - 30^{0} = 30^{0}$

Given that $| \to A |$ and $| \to B | = 10 u n i t s$

Hence, magnitude of resultant is,

$R = \sqrt{(A^{2} + B^{2} + 2 A B c o s θ)}$

$= \sqrt{(10^{2} + 10^{2} + 2 \times 10 \times 10 c o s 30^{0})}$

$= \sqrt{(200 + 200 \times \sqrt{3 / 2}}$

Resultant, $R = 19.32 u n i t s$ .

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