Let the arc AC of a circle subtend a right angle at the centre O. If the point B on the arc AC, divides the arc AC such that (length of arc AB)/(length of arc BC) = 1/5, and OC = α OA + β OB, then α + √(2)(√(3) - 1) β is equal to

Vector Algebra: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q10

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumVector Algebra184× since 2002

Let the arc

AC

of a circle subtend a right angle at the centre

O

. If the point

B

on the arc

AC

, divides the arc

AC

such that

\frac{\text{length of arc } AB}{\text{length of arc } BC} = \frac{1}{5}

, and

\overrightarrow{OC} = \alpha \overrightarrow{OA} + \beta \overrightarrow{OB}

, then

\alpha + \sqrt{2}(\sqrt{3} - 1) \beta

is equal to