JEE Advanced 2017 · Paper 2 · Mathematics Q15

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MathematicsSingle correct+3Question 51 of 54

Passage

PARAGRAPH 1

Let $O$ be the origin, and $\overrightarrow{OX}$ , $\overrightarrow{OY}$ , $\overrightarrow{OZ}$ be three unit vectors in the directions of the sides $\overrightarrow{QR}$ , $\overrightarrow{RP}$ , $\overrightarrow{PQ}$ , respectively, of a triangle $PQR$ .

$|\overrightarrow{OX} \times \overrightarrow{OY}| =$

\sin(P + Q)

\sin 2R

\sin(P + R)

\sin(Q + R)

Answer and worked solution

Official answer: A

The angle between the directions $\overrightarrow{QR}$ and $\overrightarrow{RP}$ is $\pi-R$ . So
$|\overrightarrow{OX}\times\overrightarrow{OY}|=\sin(\pi-R)=\sin R=\sin(P+Q).$

(A)

Topics:Cross product Trigonometric ratios and identities

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JEE Advanced 2017 · Paper 2, Mathematics question 15