Let a → = 5 i ^ - j ^ - 3 k ^ and b → = i ^ + 3 j ^ + 5 k ^ be two vectors. Then which one of…

Let a→=5i^-j^-3k^ and b→=i^+3j^+5k^ be two vectors. Then which one of the following statements is TRUE?
  1. Projection of a→ on b→ is -1335 and the direction of the projection vector is opposite to the direction of b→
  2. Projection of a→ on b→ is -1735 and the direction of the projection vector is opposite to the direction of b→
  3. Projection of a→ on b→ is 1735 and the direction of the projection vector is opposite to the direction of b→
  4. Projection of a→ on b→ is 1335 and the direction of the projection vector is opposite to the direction of a→

Solution

Given

a→=5i^-j^-3k^

So, a→=52+12+32=35

b→=i^+3j^+5k^

So, 52+12+32=35

So, a→·b→=5-3-15=-13

Now finding the projection of a→ on b→ using the formula we get,

a→·b→b→=-1335

And projection of b→ on a→ is given by,

a→·b→a→=-1335

Note- The original answer key was dropped by NTA in Jee mains 1st feb 2023, here we have modified the options.

Asked in: JEE Main 2023 (01 Feb Shift 2)

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