Two vectors of equal magnitude 5 unit have an angle 60^0 between them. magnitude of a sum of vectors

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3-1.Vectors

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Two vectors of equal magnitude $5$ unit have an angle $60^0$ between them. Find the magnitude of a the sum of the vectors and b the difference of the vectors.

A$2\sqrt 3 \,\,$ and $ \,9{0^ \circ }$

B$3\sqrt 3 \,\,$ and $\,6{0^ \circ }$

C$5\sqrt 3 \,$ and $\,3{0^ \circ }$

D$4\sqrt 3 \,\,$ and $\,9{0^ \circ }$

Solution

$a = 5$ and $ \theta = 60^0 $
$R = \sqrt {{a^2} + {a^2} + 2a.a \cos 60^\circ } = a\sqrt 3 = 5\sqrt 3 $
$\tan \alpha = \frac{{a \sin 60^\circ }}{{a + \; a\cos 60^\circ }} = \frac{{\frac{{\sqrt 3 }}{2}}}{{\frac{3}{2}}} = \frac{1}{{\sqrt 3 }} = \tan 30^\circ $
$ \therefore \alpha = {\text{30}}^\circ $

Standard 11

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Two vectors of equal magnitude $5$ unit have an angle $60^0$ between them. Find the magnitude of a the sum of the vectors and b the difference of the vectors.

Solution

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