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JEE Main 28-Jan-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 28-Jan-2025 Paper - Shift 24 Marks
MCQ
Let $A, B, C$ be three points in xy-plane, whose position vector are given by $\sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt{3} \hat{j}$ and $a \hat{i}+(1-a) \hat{j}$ respectively with respect to the origin O . If the distance of the point C from the line bisecting the angle between the vectors $\overrightarrow{\mathrm{OA}}$ and $\overrightarrow{\mathrm{OB}}$ is $\frac{9}{\sqrt{2}}$, then the sum of all the possible values of a is :
  • A
    1
  • B
    $9 / 2$
  • D
    2
✓

Answer

A.
Equation of angle bisector: $x-y=0$
$\left|\frac{ a (1- a )}{\sqrt{2}}\right|=\frac{9}{\sqrt{2}} \Rightarrow a =5$ or -4
Sum $=5+(- 4)=1$

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