If the line segment joining the points (5,2) and (2, a) subtends an angle π/4 at the origin, then the absolute value of the product of all possible values of a is:

Mathematics · Straight lines

JEE Main 2024 — 8 April, Shift 2 — Question 12

If the line segment joining the points $(5,2)$ and (2, a) subtends an angle $\frac{\pi}{4}$ at the origin, then the absolute value of the product of all possible values of a is:

Option A:
6
Option B:
8
Option C:
2
Option D:
4
Correct

Answer: D

Step-by-step solution

$\mathrm{m}_{\mathrm{OA}}=\frac{2}{5}$

$\mathrm{m}_{\text {OB }}=\frac{\mathrm{a}}{2}$

$\tan \frac{\pi}{4}=\left|\frac{2}{5}-\frac{\mathrm{a}}{2}\right|$

$1=\left|\frac{4-5 a}{10+2 a}\right|$

$-\frac{6}{7} \times \frac{14}{3}=-4$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 8 April, Shift 2
Subject: Mathematics
Chapter: Straight lines
Topic: Angle between lines, perpendicular distance & distance between parallel lines, foot, image

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