MHT CET · Maths · Vector Algebra
If the vectors \(\hat{\imath}+\hat{\jmath}+\hat{k}, \hat{\imath}-\hat{\jmath}+\hat{k}\) and \(2 \hat{\imath}+3 \hat{\jmath}+m \hat{k}\) are coplanar, then \(m=\)
- A 3
- B -2
- C 2
- D -3
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
(C)
Since given vectors are coplanar, we write
\(\begin{array}{l}
\left|\begin{array}{ccc}
1 & 1 & 1 \\
1 & -1 & 1 \\
2 & 3 & \mathrm{~m}
\end{array}\right|=0\end{array}\)
\(\therefore(-\mathrm{m}-3)-(\mathrm{m}-2)+(3+2)=0 \Rightarrow 2 \mathrm{~m}=4 \Rightarrow \mathrm{m}=2\)
Since given vectors are coplanar, we write
\(\begin{array}{l}
\left|\begin{array}{ccc}
1 & 1 & 1 \\
1 & -1 & 1 \\
2 & 3 & \mathrm{~m}
\end{array}\right|=0\end{array}\)
\(\therefore(-\mathrm{m}-3)-(\mathrm{m}-2)+(3+2)=0 \Rightarrow 2 \mathrm{~m}=4 \Rightarrow \mathrm{m}=2\)
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