MHT CET · Maths · Vector Algebra
The value of \(m\), if the vectors \(\hat{\imath}-\hat{\jmath}-6 \hat{k}, \hat{\imath}-3 \hat{\jmath}+4 \hat{k}\) and \(2 \hat{\imath}-5 \hat{\jmath}+m \hat{k}\) are coplanar, is
- A 1
- B \(-3\)
- C 3
- D \(-1\)
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
\(\bar{a}=\hat{i}-\hat{j}-6 \hat{k}, \bar{b}=\hat{i}-3 \hat{j}+4 \hat{k}, \bar{c}=2 \hat{i}-5 \hat{j}+m \hat{k}\) are coplanar
\(\therefore\left|\begin{array}{rrr}1 & -1 & -6 \\ 1 & -3 & 4 \\ 2 & -5 & m\end{array}\right|=0\)
\(1(-3 m+20)+1(m-8)-6(-5+6)=0\)
\(-3 m+20+ m -8+30-36=0 \Rightarrow-2 m+6=0 \Rightarrow m=3\)
\(\therefore\left|\begin{array}{rrr}1 & -1 & -6 \\ 1 & -3 & 4 \\ 2 & -5 & m\end{array}\right|=0\)
\(1(-3 m+20)+1(m-8)-6(-5+6)=0\)
\(-3 m+20+ m -8+30-36=0 \Rightarrow-2 m+6=0 \Rightarrow m=3\)
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