MHT CET · Maths · Vector Algebra
For any two non-zero vectors \(\bar{a}\) and \(\bar{b},(a \bar{b}+b \bar{a}) \cdot(a \bar{b}-b \bar{a})\) is
- A \(2|\overline{\mathrm{b}}| 2\)
- B \(0\)
- C \(|\overline{\mathrm{a}}|^2\)
- D \(|\overline{\mathrm{a}}|^2+|\overline{\mathrm{b}}|^2\)
Answer & Solution
Correct Answer
(B) \(0\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (a \vec{b}+b \vec{a}) \cdot(a \vec{b}-b \vec{a}) \\ & =a^2(\vec{b} \cdot \vec{b})-b^2(\vec{a} \cdot \vec{a}) \\ & =a^2 b^2-b^2 a^2 \\ & =0\end{aligned}\)
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