COMEDK · Maths · 33. Vector Algebra
If \(\mathbf{a}\) and \(\mathbf{b}\) are the two vectors such that \(|\mathrm{a}|=3 \sqrt{3},|b|=4\) and \(|\mathrm{a}+\mathrm{b}|=\sqrt{7}\), the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is
- A \(150^{\circ}\)
- B \(30^{\circ}\)
- C \(60^{\circ}\)
- D \(120^{\circ}\)
Answer & Solution
Correct Answer
(A) \(150^{\circ}\)
Step-by-step Solution
Detailed explanation
We have, \(|a|=3 \sqrt{3},|b|=4\) and \(|\mathbf{a}+b|=\sqrt{7}\) Now, \(|\mathbf{a}+\mathbf{b}|^{2}=|\mathbf{a}|^{2}+|\mathbf{b}|^{2}+2|\mathbf{a}||\mathbf{b}| \cos \theta\) \(\Rightarrow \quad(\sqrt{7})^{2}=(3 \sqrt{3})^{2}+16+2(3 \sqrt{3})(4) \cos \theta\)…
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