JEE Main202311 Apr 2023Evening ShiftMathematicsVector AlgebraActual
If four distinct points with position vectors a → , b → , c → and d → are coplanar, then [ a → b → c → ] is equal to
Options
- Ad → b → a → + a → c → d → + d → b → c →
- Ba → d → b → + d → c → a → + d → b → c →
- Cd → c → a → + b → d → a → + c → d → b →
- Db → c → d → + d → a → c → + d → b → a →
Correct answer
C. d → c → a → + b → d → a → + c → d → b →
Step-by-step solution
Given that a → , b → , c → , d → are coplanar. ⇒ b → - a → , c → - a → , d → - a → are also coplanar. ⇒ b → - a → c → - a → d → - a → = 0 ⇒ b → - a → . c → - a → × d → - a → = 0 ⇒ b → - a → . c → × d → - c → × a → - a → × d → = 0               ( Since   a