Let vec a=hat i+2hat j+hat k and vec b=2hat i+7hat j+3hat k . Let L_1:vec r= (-hat i+2hat j+hat k )+lambdavec a , lambdainmathbf R and L_2:vec r= (hat j+hat k )+muvec b , muinmathbf R be two lines. If the line L_3 passes through the point of intersection of L_1 and L_2 , and is parallel to vec a+vec b , then L_3 passes through the point :

Vector Algebra: Let vec a=hat i+2hat j+hat k and vec b=2hat i+7hat j+3hat k . Let… | JEE Main 2025

JEE Main 2025 (Online) 29th January Morning ShiftQuestion 1

Let $\vec a=\hat i+2\hat j+\hat k$ and $\vec b=2\hat i+7\hat j+3\hat k$. Let $L_1:\vec r=\left(-\hat i+2\hat j+\hat k\right)+\lambda\vec a$, $\lambda\in\mathbf R$ and $L_2:\vec r=\left(\hat j+\hat k\right)+\mu\vec b$, $\mu\in\mathbf R$ be two lines. If the line $L_3$ passes through the point of intersection of $L_1$ and $L_2$, and is parallel to $\vec a+\vec b$, then $L_3$ passes through the point :

Vector Algebra

$(5,17,4)$$(2,8,5)$$(8,26,12)$✓ Correct answer$(-1,-1,1)$

Solution

$L_1:(-1+\lambda,2+2\lambda,1+\lambda)$, $L_2:(2\mu,1+7\mu,1+3\mu)$ meet at $\lambda=3,\mu=1$, point $(2,8,4)$. $L_3:(2+3t,8+9t,4+4t)$; $t=2$ gives $(8,26,12)$.

Vector Algebra - JEE Mathematics question (JEE Main 2025 (Online) 29th January Morning Shift)

More from Vector Algebra