MHT CET · Maths · Vector Algebra
If the vectors \(m \hat{i}+m \hat{j}+n \hat{k}, \hat{i}+\hat{k}, n \hat{i}+n \hat{j}+p \hat{k}\) lie in a plane then...
- A \(m+n+p=0\)
- B \(\mathrm{m}, \mathrm{n}, \mathrm{p}\) are in A.P.
- C \(\mathrm{m}, \mathrm{n}, \mathrm{p}\) are in G.P.
- D \(\mathrm{n}, \mathrm{m}, \mathrm{p}\) are in G.P.
Answer & Solution
Correct Answer
(C) \(\mathrm{m}, \mathrm{n}, \mathrm{p}\) are in G.P.
Step-by-step Solution
Detailed explanation
\(\begin{vmatrix} m & m & n \\ 1 & 0 & 1 \\ n & n & p \end{vmatrix} = 0\) \(m(0 \cdot p - 1 \cdot n) - m(1 \cdot p - 1 \cdot n) + n(1 \cdot n - 0 \cdot n) = 0\)
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