Three particles P ,   Q and R are moving along the vectors A → = i ^ + j ^ ,    B…

Three particles P, Q and R are moving along the vectors A→=i^+j^,  B→=j^+k^ and C→=-i^+j^, respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane which contains vector A→ and B→. Similarly particle Q is moving normal to the plane which contains vector A→ and C→. The angle between the direction of motion of P and Q is cos-11x. Then the value of x is          .

Solution

Direction of P, v^1=±A→×B→|A→×B→|=±i^-j^+k^3

Direction of Q, v^2=±A→×C→|A→×C→|=±2k^2=±k^

Angle between v^1 and v^2,

v^1·v^2v^1v^2=±13(1)(1)=±13

⇒x=3

Asked in: JEE Main 2021 (22 Jul Shift 1)

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