MHT CET · Maths · Vector Algebra
If â is a unit vector such that \((\bar{x}-\hat{a}) \cdot(\bar{x}+\hat{a})=8\), then \(|\bar{x}|=\)
- A \(\pm 3\)
- B \(2 \sqrt{2}\)
- C 3
- D \(\pm \sqrt{7}\)
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
We have \((\overline{\mathrm{x}}-\hat{\mathrm{a}}) \cdot(\overline{\mathrm{x}}+\hat{\mathrm{a}})=8\)
\(
\therefore|\overline{\mathrm{x}}|^2-|\hat{\mathrm{a}}|^2=8 \Rightarrow|\overline{\mathrm{x}}|^2=8+1=9 \Rightarrow|\overline{\mathrm{x}}|=3
\)
\(
\therefore|\overline{\mathrm{x}}|^2-|\hat{\mathrm{a}}|^2=8 \Rightarrow|\overline{\mathrm{x}}|^2=8+1=9 \Rightarrow|\overline{\mathrm{x}}|=3
\)
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