JEE Mains · Maths · STD 12 - 10. vector algebra
If \((\vec{a}+3 \vec{b})\) is perpendicular to \((7 \vec{a}-5 \vec{b})\) and \((\vec{a}-4 \vec{b})\) is perpendicular to \((7 \vec{a}-2 \vec{b})\), then the angle between \(\vec{a}\) and \(\vec{b}\) (in degrees) is \(......\)
- A \(40\)
- B \(60\)
- C \(15\)
- D \(75\)
Answer & Solution
Correct Answer
(B) \(60\)
Step-by-step Solution
Detailed explanation
\((\vec{a}+3 \vec{b}) \perp(7 \vec{a}-5 \vec{b})\) \((\vec{a}+3 \vec{b}) \cdot(7 \vec{a}-5 \vec{b})=0\) \(7|\vec{a}|^{2}-15|\vec{b}|^{2}+16 \vec{a} \cdot \vec{b}=0 \ldots(1)\) \((\vec{a}-4 \vec{b}) \cdot(7 \vec{a}-2 \vec{b})=0\)…
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