jee-main 2023 Q75

jee-main · India · session2_10apr_shift1 Vectors Introduction & 2D Expressing a Vector as a Linear Combination

An arc $PQ$ of a circle subtends a right angle at its centre $O$. The mid point of the arc $PQ$ is $R$. If $\overrightarrow{OP} = \vec{u}$, $\overrightarrow{OR} = \vec{v}$ and $\overrightarrow{OQ} = \alpha\vec{u} + \beta\vec{v}$, then $\alpha$, $\beta^2$ are the roots of the equation
(1) $x^2 + x - 2 = 0$
(2) $x^2 - x - 2 = 0$
(3) $3x^2 - 2x - 1 = 0$
(4) $3x^2 + 2x - 1 = 0$

An arc $PQ$ of a circle subtends a right angle at its centre $O$. The mid point of the arc $PQ$ is $R$. If $\overrightarrow{OP} = \vec{u}$, $\overrightarrow{OR} = \vec{v}$ and $\overrightarrow{OQ} = \alpha\vec{u} + \beta\vec{v}$, then $\alpha$, $\beta^2$ are the roots of the equation\\
(1) $x^2 + x - 2 = 0$\\
(2) $x^2 - x - 2 = 0$\\
(3) $3x^2 - 2x - 1 = 0$\\
(4) $3x^2 + 2x - 1 = 0$

Paper Questions

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