JEE Main202429 Jan 2024Evening ShiftMathematicsThree Dimensional GeometryActual

Let P ( 3 , 2 , 3 ) , Q ( 4 , 6 , 2 ) and R ( 7 , 3 , 2 ) be the vertices of ∆ PQR . Then, the angle ∠ QPR is

Options

Aπ 6
Bcos - 1 7 18
Ccos - 1 1 18
Dπ 3

Correct answer

D. π 3

Step-by-step solution

Given, ⇒ QP → = - i ^ - 4 j ^ + k ^ and RP → = - 4 i ^ - j ^ + k ^ cos ∠ QPR = QP → · RP → QP → RP → ⇒ cos ∠ QPR = 4 + 4 + 1 1 + 16 + 1 16 + 1 + 1 ⇒ cos ∠ QPR = 9 18 = 1 2 ⇒ ∠ QPR = π 3

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