MHT CET · Maths · Vector Algebra
The volume of the tetrahedron having vertices \((1,-6,10)\), \((-1,-3,7),(5,-1, \lambda)\) and \((7,-4,7)\) is \(11 \mathrm{cu}\). Units, then \(\lambda=\)
- A 3
- B 1
- C 5
- D 7
Answer & Solution
Correct Answer
(D) 7
Step-by-step Solution
Detailed explanation
\(\text{Volume of a tetrahedron}\) \(=\frac{1}{6}\left|\begin{array}{lll}x_2-x_1 & y_2-y_1 & z_2-z_1 \\ x_3-x_1 & y_3-y_1 & z_3-z_1 \\ x_4-x_1 & y_4-y_1 & z_4-z_1\end{array}\right|\)
\(=\frac{1}{6}\left|\begin{array}{ccc}-2 & 3 & -3 \\ 4 & 5 & \lambda-10 \\ 6 & 2 & -3\end{array}\right|\)
\(\Rightarrow 11=\frac{1}{6}\{22 \lambda-88\} \Rightarrow \lambda=7\)
\(=\frac{1}{6}\left|\begin{array}{ccc}-2 & 3 & -3 \\ 4 & 5 & \lambda-10 \\ 6 & 2 & -3\end{array}\right|\)
\(\Rightarrow 11=\frac{1}{6}\{22 \lambda-88\} \Rightarrow \lambda=7\)
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