Let $\vec a$ and $\vec b$ be two unit vectors such that the angle between them is $\frac\pi3$. 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 :

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] $(\lambda\vec a+2\vec b)\cdot(3\vec a-\lambda\vec b)=3\lambda-\frac{\lambda^2}2+3-2\lambda=0\Rightarrow\lambda^2-2\lambda-6=0$, so $\lambda=1\pm\sqrt7\approx3.65,\,-1.65$. Neither lies in $[-1,3]$, so there are no such values. Answer (3).

Q. Let $\vec a$ and $\vec b$ be two unit vectors such that the angle between them is $\frac\pi3$. 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 :

Explanation

Reviewed by Dr. Abubacker

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