Maths · Scalar and vector products
For any four points is equal to 4 times the area of the triangle.
For any four points \( P, Q, R, S \) \( |\overrightarrow{P Q} \times \overrightarrow{\boldsymbol{R}} \boldsymbol{S}-\overrightarrow{\boldsymbol{Q} \boldsymbol{R}} \times \overrightarrow{\boldsymbol{P}} \boldsymbol{S}+\overrightarrow{\boldsymbol{R}} \boldsymbol{P} \times \overrightarrow{\boldsymbol{Q}} \boldsymbol{S}| \) is equal to 4 times the area of the triangle.
- A. PQR
- B. QRS
- C. PRS
- D. PQS
Step-by-step solution
The expression simplifies to 2|R̂Q × R̂S| = 4 × area of triangle QRS. Hence, the correct option is B.
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