A) 1
B) 2
C) 3
D) 4
Correct Answer: A
Solution :
Let\[\overrightarrow{\mathbf{a}}=\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}-\widehat{\mathbf{k}},\,\,\overrightarrow{\mathbf{b}}=\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}}\] and\[\overrightarrow{\mathbf{c}}=\widehat{\mathbf{i}}-\widehat{\mathbf{j}}+\lambda \widehat{\mathbf{k}}\] Since, volume of tetrahedron\[=\frac{1}{6}[\overrightarrow{\mathbf{a}}\overrightarrow{\mathbf{b}}\overrightarrow{\mathbf{c}}]\] \[\Rightarrow \] \[\frac{2}{3}=\frac{1}{6}\left| \begin{matrix} 1 & 2 & -1 \\ 1 & 1 & 1 \\ 1 & -1 & \lambda \\ \end{matrix} \right|\] \[\Rightarrow \] \[\frac{2}{3}=\frac{1}{6}[1(\lambda +1)-2(\lambda -1)-1(1-1)]\] \[\Rightarrow \] \[4=[-\lambda +5]\] \[\Rightarrow \] \[\lambda =1\]You need to login to perform this action.
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