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Q.

Two vectors having equal magnitude of $5$ units, have an angle of $60 °$ between them. Find the magnitude of their resultant vector and its angle from one of the vectors.

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a

$5 \sqrt{3} u n i t,$ $α = 30 °$

b

$5 \sqrt{3} u n i t, α = 60 °$

c

$3 \sqrt{5} unit, α = 45 °$

d

$3 \sqrt{5} unit, α = 90 °$

answer is A.

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Detailed Solution

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$a = b = 5 u n i t$ and $θ = 60 °$

$R = \sqrt{a^{2} + a^{2} + 2 a^{2} \cdot \cos (60 °)} = a \sqrt{3} = 5 \sqrt{3} u n i t$

$\tan (α) = \frac{a \sin (60 °)}{a + a \cos (60 °)} = \frac{\frac{\sqrt{3}}{2}}{\frac{3}{2}} = \frac{1}{\sqrt{3}} o r \tan (30 °)$

Therefore, $α = 30 °$

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Two vectors having equal magnitude of 5 units, have an angle of 60° between them. Find the magnitude of their resultant vector and its angle from one of the vectors.