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JEE Main20231 Feb 2023Evening ShiftMathematicsVector AlgebraActual

Let a → = 5 i ^ - j ^ - 3 k ^ and b → = i ^ + 3 j ^ + 5 k ^ be two vectors. Then which one of the following statements is TRUE?

Options

  1. AProjection of a → on b → is - 13 35 and the direction of the projection vector is opposite to the
  2. BProjection of a → on b → is - 17 35 and the direction of the projection vector is opposite to the
  3. CProjection of a → on b → is 17 35 and the direction of the projection vector is opposite to the di
  4. DProjection of a → on b → is 13 35 and the direction of the projection vector is opposite to the di

Correct answer

A. Projection of a → on b → is - 13 35 and the direction of the projection vector is opposite to the

Step-by-step solution

Given a → = 5 i ^ - j ^ - 3 k ^ So, a → = 5 2 + 1 2 + 3 2 = 35 b → = i ^ + 3 j ^ + 5 k ^ So, 5 2 + 1 2 + 3 2 = 35 So, a → · b → = 5 - 3 - 15 = - 13 Now finding the projection of a → on b → using the formula we get, a → · b → b → = - 13 35 And projection of b → on a → is given by, a → · b → a → = - 13 35 Note- The original answer key was dropped by NTA in Jee mains 1st feb 2023, here we have modified the options.

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