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JEE Main202117 Mar 2021Evening ShiftMathematicsVector AlgebraActual

Let x → be a vector in the plane containing vectors a → = 2 i ^ - j ^ + k ^ and b → = i ^ + 2 j ^ - k ^ . If the vector x → is perpendicular to ( 3 i ^ + 2 j ^ - k ^ ) and its projection on a → is 17 6 2 , then the value of x → 2 is equal to _______.

Correct answer

0

Step-by-step solution

A plane containing two vectors can be expressed as a linear combination of the vectors. Hence, let x → = λ a → + μ b →   ( λ and μ are scalars ) . ⇒ x → = i ^ ( 2 λ + μ ) + j ^ ( 2 μ - λ ) + k ^ ( λ - μ ) Since x → is perpendicular to 3 i ^ + 2 j ^ - k ^ , ⇒ x → · 3 i ^ + 2 j ^ - k ^ = 0 ⇒ i ^ ( 2 λ + μ ) + j ^ ( 2 μ - λ ) + k ^ ( λ - μ ) · 3 i ^ + 2 j ^ - k ^ = 0 &#86

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