a-b-40-a-b-20-amp-a-10-then-find-b-

Question Number 28695 by yesaditya22@gmail.com last updated on 29/Jan/18

∣ \vec{a} + \vec{b} ∣= 40, ∣ \vec{a} - \vec{b} ∣= 20 & ∣ \vec{a} ∣= 10 then find ∣ \vec{b} ∣

Answered by mrW2 last updated on 29/Jan/18

40^{2} = a^{2} + b^{2} - 2 a b \cos θ

20^{2} = a^{2} + b^{2} - 2 a b \cos (180 - θ)

20^{2} = a^{2} + b^{2} + 2 a b \cos θ

b^{2} = \frac{40^{2} + 20^{2}}{2} - a^{2} = \frac{40^{2} + 20^{2}}{2} - 10^{2} = 900

\Rightarrow b = \sqrt{900} = 30

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