AP EAMCET · Maths · Vector Algebra
If \(\mathbf{a}\) and \(\mathbf{b}\) are two non-collinear vectors and the vector \(\mathbf{a}+\mathbf{b}\) bisects the angle between \(\mathbf{a}\) and \(\mathbf{b}\), then
- A \(|\mathbf{a}|=|\mathbf{b}|\)
- B angle between \(\mathbf{a}, \mathbf{b}\) is \(0^{\circ}\) (or) \(\pi\)
- C a , b always form adjacent sides of a square.
- D a, b always form adjacent sides of a rectangle.
Answer & Solution
Correct Answer
(A) \(|\mathbf{a}|=|\mathbf{b}|\)
Step-by-step Solution
Detailed explanation
Here, \(O A=|\mathbf{a}|\) \(O D=A C=|\mathbf{b}|\) \(\begin{aligned} & \text { In } \triangle A B C, A B=|\mathbf{b}| \cos 2 \theta \\ & \text { and } B C=|\mathbf{b}| \sin 2 \theta \\ & \text { In } \triangle O B C \text {, }\end{aligned}\)…
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