JEE Mains · Maths · STD 12 - 10. vector algebra
An are \(P Q\) of a circle subtends a right angle at its centre \(O\). The mid point of the arc \(P Q\) is \(R\). If \(\overline{O P}=\vec{u}, \overline{O R}=\vec{v}\) and \(\overrightarrow{O Q}=\alpha \vec{u}+\beta \vec{v}\), then \(\alpha, \beta^2\) are the roots of the equation
- A \(x ^2- x -2=0\)
- B \(3 x^2+2 x-1=0\)
- C \(x^2+x-2=0\)
- D \(3 x ^2-2 x -1=0\)
Answer & Solution
Correct Answer
(A) \(x ^2- x -2=0\)
Step-by-step Solution
Detailed explanation
\(|\vec{u}|=|\vec{v}|=|\alpha \vec{u}+\beta \vec{v}|\) \((\vec{u}) \cdot(\alpha \vec{u}+\beta \vec{v})=0\) \(\vec{u} \cdot \vec{v}=|u||v| \cos 45^{\circ}\) \(\alpha=-\frac{\beta}{\sqrt{2}}\) \(=|\alpha \vec{u}+\beta \vec{v}|=r\) \(\alpha^2+\beta^2+\sqrt{2} \alpha \beta=1\)…
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