Straight Lines
Angle Between Two Lines
JEE Main 2024
Grade 11
Question:
If the line segment joining $(5, 2)$ and $(2, a)$ subtends an angle $\pi/4$ at the origin, find the absolute value of the product of all possible values of $a$.
Step-by-Step Solution
Key Concept: Use $\tan(\angle AOB) = \left|\frac{m_1 - m_2}{1 + m_1m_2}\right| = 1$ where $m_1 = 2/5$ and $m_2 = a/2$. This gives a linear equation in $a$ for each $\pm$ case — find both roots.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 4