TS EAMCET · Maths · Vector Algebra
If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are three mutually perpendicular vectors such that the magnitudes of \(\mathbf{b}\) and \(\mathbf{c}\) are \(1 / 2\) times and \(\sqrt{3} / 2\) times that of \(\mathbf{a}\), respectively, then the angle between the vectors \(\mathbf{a}+\mathbf{b}+\mathbf{c}\) and \(\mathbf{b}\) is
- A \(45^{\circ}\)
- B \(\cos ^{-1}\left(\frac{1}{2 \sqrt{2}}\right)\)
- C \(\cos ^{-1}\left(\frac{\sqrt{6}}{4}\right)\)
- D \(\cos ^{-1}\left(\frac{1}{4}\right)\)
Answer & Solution
Correct Answer
(B) \(\cos ^{-1}\left(\frac{1}{2 \sqrt{2}}\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, }|\mathbf{b}|=\frac{1}{2}|\mathbf{a}| \text { and }|\mathbf{c}|=\frac{\sqrt{3}}{2}|\mathbf{a}| \\ & \text { and } \quad \begin{aligned} \mathbf{a} \cdot \mathbf{b} & =\mathbf{b} \cdot \mathbf{c}=\mathbf{a} \cdot \mathbf{c}=0 \\…
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