A vector `barQ `which has a magnitude of 8 is added to the vector `barP` which lies along the X-axis. The resultant of these two vectors is a third vector `barR ` which lies along the Y-axis and has a magnitude twice that of `barP`. The magnitude of `barP` is

Explanation

To solve the problem, we need to find the magnitude of vector \( \bar{P} \). We know the following:

1. The magnitude of vector \( \bar{Q} \) is 8.
2. Vector \( \bar{P} \) lies along the X-axis.
3. The resultant vector \( \bar{R} \) lies along the Y-axis and has a magnitude that is twice that of \( \bar{P} \).

Let's denote the magnitude of vector \( \bar{P} \) as \( p \). Therefore, the magnitude of vector \( \bar{R} \) is \( 2p \).

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