MHT CET · Maths · Vector Algebra
If \(\theta\) is an obtuse angle between vector \(\overline{\mathrm{a}}\) and \(\overline{\mathrm{b}}\) such that \(|\overline{\mathrm{a}}|=5,|\overline{\mathrm{~b}}|=3\) and \(|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|=5 \sqrt{5}\) then \(\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=\)
- A \(10\)
- B \(-10\)
- C \(5\)
- D \(-5\)
Answer & Solution
Correct Answer
(B) \(-10\)
Step-by-step Solution
Detailed explanation
\(\sin\theta = \frac{|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|}{|\overline{\mathrm{a}}||\overline{\mathrm{b}}|} = \frac{5 \sqrt{5}}{5 \times 3} = \frac{\sqrt{5}}{3}\) \(\cos^2\theta = 1 - \sin^2\theta = 1 - \left(\frac{\sqrt{5}}{3}\right)^2 = 1 - \frac{5}{9} = \frac{4}{9}\)
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