JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors such that the angle between them is \(\frac{\pi}{3}\). If \(\lambda \vec{a}+2 \vec{b}\) and \(3 \vec{a}-\lambda \vec{b}\) are perpendicular to each other, then the number of values of \(\lambda\) in \([-1,3]\) is :
- A 2
- B 1
- C 0
- D 3
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
\begin{aligned} & \hat{a} \cdot \hat{b}=\frac{1}{2} \\ & \text { Now }(\lambda \hat{a}+2 \hat{b}) \cdot(3 \hat{a}-\lambda \hat{b})=0 \\ & 3 \lambda \hat{a} \cdot \hat{a}-\lambda^2 \hat{a} \cdot \hat{b}+6 \hat{a} \cdot \hat{b}-2 \lambda \hat{b} \cdot \hat{b}=0 \\ & 3…
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