If $ |\vec{a}|=7,|\vec{b}|=11,|\vec{a}+\vec{b}|=10 \sqrt{3} $, then $ |\vec{a}-\vec{b}| $ equals

Question

If $ |\vec{a}|=7,|\vec{b}|=11,|\vec{a}+\vec{b}|=10 \sqrt{3} $, then $ |\vec{a}-\vec{b}| $ equals, $ 10 $, $ \sqrt{10} $, $ 2 \sqrt{10} $, $ 20 $

MARKS App · Accepted Answer

Given: a → = 7 b → = 11 a → + b → = 10 3 Now, we have, a → + b → 2 + a → - b → 2 = a → 2 + b → 2 + 2 a → · b → + a → 2 + b → 2 - 2 a → · b → ⇒ a → + b → 2 + a → - b → 2 = 2 a → 2 + b → 2 ⇒ 300 + a → - b → 2 = 2 49 + 121 ⇒ a → - b → = 2 10

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