AP EAMCET · Maths · Three Dimensional Geometry
If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are vectors of equal magnitude such that \((\mathbf{a}, \mathbf{b})=\alpha,(\mathbf{b}, \mathbf{c})=\beta,(\mathbf{c}, \mathbf{a})=\gamma\), then the minimum value of \(\cos \alpha+\cos \beta+\cos \gamma\) is
- A \(\frac{3}{2}\)
- B \(-\frac{3}{2}\)
- C \(\frac{1}{2}\)
- D \(-\frac{1}{2}\)
Answer & Solution
Correct Answer
(B) \(-\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
We have, \(\cos \alpha=\frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}||\mathbf{b}|}, \cos \beta=\frac{\mathbf{b} \cdot \mathbf{c}}{|\mathbf{b}||\mathbf{c}|}\) and \(\cos \gamma=\frac{\mathbf{c} \cdot \mathbf{a}}{|\mathbf{c}||\mathbf{a}|}\) Also, it is given that…
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