MHT CET · Maths · Vector Algebra
The sum of the distinct real values of \(\mu\), for which the vector \(\mu \hat{i}+\hat{j}+\hat{k}, \hat{i}+\mu \hat{j}+\hat{k}, \hat{i}+\hat{j}+\mu \hat{k}\) are coplanar is
- A 1
- B -1
- C 2
- D 0
Answer & Solution
Correct Answer
(B) -1
Step-by-step Solution
Detailed explanation
From the condition for co-planarity
\(\begin{aligned}
& \left|\begin{array}{lll}
\mu & 1 & 1 \\
1 & \mu & 1 \\
1 & 1 & \mu
\end{array}\right|=0 \\
& \Rightarrow(2+\mu)(\mu-1)^2=0 \\
& \Rightarrow \mu=-2 \text { or } \mu=1 \\
& \text { sum }=-2+1=-1
\end{aligned}\)
\(\begin{aligned}
& \left|\begin{array}{lll}
\mu & 1 & 1 \\
1 & \mu & 1 \\
1 & 1 & \mu
\end{array}\right|=0 \\
& \Rightarrow(2+\mu)(\mu-1)^2=0 \\
& \Rightarrow \mu=-2 \text { or } \mu=1 \\
& \text { sum }=-2+1=-1
\end{aligned}\)
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