KCET · Maths · Vector Algebra
The volume of the parallelopiped whose co terminous edges are \(\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}\) is
- A 6 cu units
- B 2 cu units
- C 4 cu units
- D 3 cu units
Answer & Solution
Correct Answer
(B) 2 cu units
Step-by-step Solution
Detailed explanation
The volume of the parallelopiped whose coterminous edges are \(\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}\) and
\(\hat{\mathbf{i}}+\hat{\mathbf{j}}=\left|\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right|\)
\(=0-1(0-1)+1(1-0)\)
\(=-1(-1)+1\)
\(=2 \mathrm{cu}\) units
\(\hat{\mathbf{i}}+\hat{\mathbf{j}}=\left|\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right|\)
\(=0-1(0-1)+1(1-0)\)
\(=-1(-1)+1\)
\(=2 \mathrm{cu}\) units
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