Q33 / 54 · JEE Advanced 2017 (Paper 2) · Mathematics

Paragraph: Let $O$ be the origin, and $\overrightarrow{O X}, \overrightarrow{O Y}, \overrightarrow{O Z}$ be three unit vectors in the directions of the sides $\overrightarrow{Q R}, \overrightarrow{R P}$, $\overrightarrow{P Q}$, respectively, of a triangle $P Q R$.
Question: $|\overrightarrow{O X} \times \overrightarrow{O Y}|=$

  • Correct answer
    A
    sinP+Q
  • B
    sin 2R
  • C
    sinP+R
  • D
    sinQ+R

Solution

OX→, OY→, OZ→ are unit vectors in the directions of sides OR→, RP→ and PQ→ respectively,

Figure

∴  OX→=QR→QR→,  OY→=RP→RP→, OZ→=PQ→PQ→ 

∴  OX→×OY→=OR→×RP→QR→ RP→

=QR→ RP→sinP+QQR→ RP→ 

=sinP+Q

Hence, the correct answer is option: 'A'.

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