AP EAMCET · Maths · Vector Algebra
If \(\theta\) is the angle between the unit vectors \(\mathbf{a}\) and \(\mathbf{b}\), then \(\sin \frac{\theta}{2}\) is equal to
- A \(\left|\frac{\mathbf{a}-\mathbf{b}}{\mathbf{a}+\mathbf{b}}\right|\)
- B \(|\mathbf{a}+\mathbf{b}|\)
- C \(|\mathbf{a}-\mathbf{b}|\)
- D \(\frac{1}{2}|\mathbf{a}-\mathbf{b}|\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2}|\mathbf{a}-\mathbf{b}|\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, }|\mathbf{a}|=|\mathbf{b}|=1 \\ & |\mathbf{a}-\mathbf{b}|^2=|\mathbf{a}|^2+|\mathbf{b}|^2-2|\mathbf{a}||\mathbf{b}| \cos \theta \\ & \Rightarrow|\mathbf{a}-\mathbf{b}|^2=1+1-2 \cos \theta \\ & \Rightarrow \quad|\mathbf{a}-\mathbf{b}|^2=2(1-\cos…
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