Q77 / 150 · MHT CET 2021 (23 Sep Shift 2) · Mathematics

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
    $2 \sqrt{2}$
  • Correct answer
    C
    3
  • D
    $\pm \sqrt{7}$

Solution

We have $(\overline{\mathrm{x}}-\hat{\mathrm{a}}) \cdot(\overline{\mathrm{x}}+\hat{\mathrm{a}})=8$ $$ \therefore|\overline{\mathrm{x}}|^2-|\hat{\mathrm{a}}|^2=8 \Rightarrow|\overline{\mathrm{x}}|^2=8+1=9 \Rightarrow|\overline{\mathrm{x}}|=3 $$

Hence, the correct answer is option: 'C'.

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