If \(\vec{OA}=\sqrt{3}\hat{ı}+\hat{ȷ},\vec{OB}=\hat{ı}+\sqrt{3}\hat{ȷ}\). If the distance of the point \(a\hat{ı}+(1-a)\…
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PYQIf \(\vec{OA}=\sqrt{3}\hat{ı}+\hat{ȷ},\vec{OB}=\hat{ı}+\sqrt{3}\hat{ȷ}\). If the distance of the point \(a\hat{ı}+(1-a)\hat{ȷ}\) from the angle bisector of \(\vec{OA}\) and \(\vec{OB}\) is \(\frac{9}{\sqrt{2}}\) the find \(a.\)
✓ Correct answer: d)
5
Explanation
Equation of anlge bisector will be
\(x-y=0\\ \left|\frac{a-(1-a)}{\sqrt{2}}\right|=\frac{9}{\sqrt{2}}\\ 2a-1=\pm 9\\ a=5,-4\)
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