Question

The resultant of two vectors`vecP` and `vecQ` is `vecR`. if the magnitude of`vecQ` is doubled , the new resultant becomes perpendicular to `vecP`. then magnitude of `vecR` is?

options are

1. =`(P+Q)`
2. =`1/2*(P+Q)`
3. =Q
4. P

Answer 1

Option 3

Explanation:

`(bbP + 2 bbQ)* bbP = 0`

• `implies P^2 = - 2 bbQ * bbP`

`bbR = bbP + bbQ`

`abs bbR^2 =( bbP + bbQ)*( bbP + bbQ)`

• `= P^2 + Q^2 + 2 bbP*bbQ`

• `= - 2 bbQ * bbP + Q^2 + 2 bbP*bbQ = Q^2`

`implies abs bbR = abs bbQ`