Q95 / 150 · MHT CET 2024 (15 May Shift 1) · Mathematics

If the vectors $\bar{a}=\hat{i}-\hat{j}+2 \hat{k}, \bar{b}=2 \hat{i}+4 \hat{j}+\hat{k}$ and $\overline{\mathrm{c}}=\mathrm{p} \hat{\mathrm{i}}+\hat{\mathrm{j}}+\mathrm{q} \hat{\mathrm{k}}$ are mutually orthogonal, then $(\mathrm{p}, \mathrm{q})$ is equal to

  • A
    $(3,-2)$
  • B
    $(-2,3)$
  • Correct answer
    C
    $(-3,2)$
  • D
    $(2,-3)$

Solution

Since the given vectors are mutually orthogonal. $\therefore \quad \bar{a} \cdot \overline{\mathrm{~b}}=2-4+2=0$ $\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=\mathrm{p}-1+2 \mathrm{q}=0$...(i) $\overline{\mathrm{b}} \cdot \overline{\mathrm{c}}=2 \mathrm{p}+4+\mathrm{q}=0$...(ii) Solving (i) and (ii), we get $(p, q)=(-3,2)$

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

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