AP EAMCET · Maths · Vector Algebra
If \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) are mutually perpendicular vectors of the same magnitude, then the cosine of the angle between \(\mathbf{a}\) and \(\mathbf{a}+\mathbf{b}+\mathbf{c}\) is
- A \(\frac{1}{\sqrt{2}}\)
- B \(\frac{1}{\sqrt{3}}\)
- C \(\frac{1}{2}\)
- D \(\frac{\sqrt{3}}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
(b) Let \(|\mathbf{a}|=|\mathbf{b}|=|\mathbf{c}|=\lambda\) Now, \(|\mathbf{a}+\mathbf{b}+\mathbf{c}|^2=(\mathbf{a}+\mathbf{b}+\mathbf{c}) \cdot(\mathbf{a}+\mathbf{b}+\mathbf{c})\)…
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