AP EAMCET · Maths · Vector Algebra
The volume (in cubic units) of the tetrahedron with edges \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) is
- A \(4\)
- B \(2 / 3\)
- C \(1 / 6\)
- D \(1 / 3\)
Answer & Solution
Correct Answer
(B) \(2 / 3\)
Step-by-step Solution
Detailed explanation
We know that, volume of tetrahedron \(\begin{aligned} & =\frac{1}{6}[\overrightarrow{\mathbf{A B}} \overrightarrow{\mathbf{A C}} \overrightarrow{\mathbf{A D}}] \\ & =\frac{1}{6}\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 2 & -1\end{array}\right|\end{aligned}\)…
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