MHT CET · Maths · Vector Algebra
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 \((-2,3)\)
- C \((-3,2)\)
- D \((2,-3)\)
Answer & Solution
Correct Answer
(C) \((-3,2)\)
Step-by-step Solution
Detailed explanation
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 \((p, q)=(-3,2)\)
\(\therefore \quad \bar{a} \cdot \overline{\mathrm{~b}}=2-4+2=0\)
\(\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=\mathrm{p}-1+2 \mathrm{q}=0\)...(i)
\(\overline{\mathrm{b}} \cdot \overline{\mathrm{c}}=2 \mathrm{p}+4+\mathrm{q}=0\)...(ii)
Solving (i) and (ii), we get \((p, q)=(-3,2)\)
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