AP EAMCET · Maths · Vector Algebra
If \(\hat{\mathbf{a}}, \hat{\mathbf{b}}\) and \(\hat{\mathbf{c}}\) are unit vectors such that \(\hat{\mathbf{a}}+\hat{\mathbf{b}}+\hat{\mathbf{c}}=\mathbf{0}\), then the \(\hat{\mathbf{a}} \cdot \hat{\mathbf{b}}+\hat{\mathbf{b}} \cdot \hat{\mathbf{c}}+\hat{\mathbf{c}} \cdot \hat{\mathbf{a}}\) is equal to
- 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
Given that \(\hat{\mathrm{a}}, \hat{\mathrm{b}}, \hat{\mathrm{c}}\) are unit vectors and \(\hat{\mathrm{a}}+\hat{\mathrm{b}}+\hat{\mathrm{c}}=0\) \(\therefore \quad|\hat{a}|=|\hat{b}|=|\hat{c}|=1\) Here, \(\hat{a}+\hat{b}+\hat{c}=\hat{0}\) Then,…
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