AP EAMCET · Maths · Vector Algebra
If \(\mathbf{a}\) and \(\mathbf{b}\) are two unit vectors such that \(\mathbf{a}+\mathbf{b}\) is also \(\mathbf{a}\) unit vector, then \(|\mathbf{a}-\mathbf{b}|^2=\)
- A 1
- B 2
- C 3
- D 0
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
If resultant of two unit vectors is unit vector, then angle between them is \(\frac{2 \pi}{3}\), so \[ \begin{aligned} |\mathbf{a}-\mathbf{b}|^2 & =|a|^2+|b|^2-2|\mathbf{a}||\mathbf{b}| \cos \frac{2 \pi}{3} \\ & =1+1-2(1)(1)(-1 / 2)=2+1=3 . \end{aligned} \]
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