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Mathematics · JEE | VECTOR ALGEBRA
हिन्दीIf \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( |\vec{a}| = 3, |\vec{b}| = 4, |\vec{c}| = 5 \) and each one of them being perpendicular to the sum of the other two, then \( |\vec{a} + \vec{b} + \vec{c}| \) is:
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Correct answer · Option A
5\( \sqrt{2} \)
Explanation
Square of magnitude is \( |\vec{a}+\vec{b}+\vec{c}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + |\vec{c}|^2 = 9 + 16 + 25 = 50 \). Thus magnitude is \( \sqrt{50} = 5\sqrt{2} \).
