WBJEE · Maths · Vector Algebra
If \(\vec{\alpha}\) is a unit vector, \(\vec{\beta}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}, \vec{\gamma}=\hat{\mathrm{i}}+\hat{\mathrm{k}}\), then the maximum value of \([\vec{\alpha} \vec{\beta} \vec{\gamma}]\) is
- A 3
- B \(\sqrt{3}\)
- C 2
- D \(\sqrt{6}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{6}\)
Step-by-step Solution
Detailed explanation
\([\vec{\alpha} \vec{\beta} \vec{\gamma}]=\vec{\alpha} \cdot(\vec{\beta} \times \vec{\gamma})=\vec{\alpha} \cdot\left|\begin{array}{ccc}\hat{i} & \hat{j} & k \\ 1 & 1 & -1 \\ 1 & 0 & 1\end{array}\right|\) \(=\vec{\alpha} \cdot(\hat{i}+2 \hat{j}-\hat{k})\) is maximum…
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