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Vector Algebra

Oswaal

CBSE

Grade 12

Question:

If $|\vec{a}| = 3, |\vec{b}| = 4, |\vec{a} + \vec{b}| = 5$, then $|\vec{a} - \vec{b}|$ is:
(a) $5$
(b) $\sqrt{7}$
(c) $1$
(d) $7$

Step-by-Step Solution

Key Concept: |a+b|^2 + |a-b|^2 = 2(|a|^2 + |b|^2) = 2(9+16) = 50 => 25 + |a-b|^2 = 50 => |a-b| = 5.

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Correct Answer: $5$

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