Q87 / 180 · JIPMER 2015 · Physics
The angle between two linear transmembrane domains is defined by following vectors $\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$
- A$\cos ^{-1}\left(\frac{1}{3}\right)$
- Correct answerB$\cos ^{-1}\left(\frac{-1}{3}\right)$
- C$\sin ^{-1}\left(\frac{-1}{3}\right)$
- D$\sin ^{-1}\left(\frac{1}{3}\right)$
Solution
The angle between two vectors is given by
$\begin{array}{rlrl} & \cos \theta & =\frac{\mathbf{a} \cdot \mathbf{b}}{a b}=\frac{1-1-1}{\sqrt{3} \times \sqrt{3}} \\ \Rightarrow & \cos \theta & =-\frac{1}{3} \\ & \therefore & \theta & =\cos ^{-1}\left(-\frac{1}{3}\right)\end{array}$
Hence, the correct answer is option: 'B'.