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Vector Algebra question

2025 · 23 Jan · Shift 1 · Q42

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JEE Main
Mathematics
Vector Algebra
2025 · 23 Jan · Shift 1 · Q42

Vector Algebra question

2025 · 23 Jan · Shift 1 · Q42

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let the arc

A C

of a circle subtend a right angle at the centre

O

. If the point

B

on the arc

A C

, divides the arc

A C

such that

\frac{\text { length of } \operatorname{arc} A B}{\text { length of } \operatorname{arc} B C}=\frac{1}{5}

, and

\overrightarrow{O C}=\alpha \overrightarrow{O A}+\beta \overrightarrow{O B}

, then

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

is equal to

A
$2 \sqrt{3}$
B
$5 \sqrt{3}$
C
$2+\sqrt{3}$
D
$2-\sqrt{3}$

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