jee-main 2025 Q10

jee-main · India · session1_22jan_shift2 Vectors Introduction & 2D Perpendicularity or Parallel Condition
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 :
(1) 2
(2) 1
(3) 0
(4) 3
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 :\\
(1) 2\\
(2) 1\\
(3) 0\\
(4) 3