TS EAMCET · Maths · Vector Algebra
If \(\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}, \quad \mathbf{b}=3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) and \(\mathbf{c}=5 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\), then the volume of the parallelopiped with coterminous edges \(\mathbf{a}+\mathbf{b}, \mathbf{b}+\mathbf{c}, \mathbf{c}+\mathbf{a}\), is
- A 1
- B 5
- C 8
- D 16
Answer & Solution
Correct Answer
(D) 16
Step-by-step Solution
Detailed explanation
We have, \(\begin{aligned} & \mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}} \\ & \mathbf{b}=3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+5 \hat{\mathbf{k}} \text { and } \mathbf{c}=5 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}} \end{aligned}\) Now,…
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