two inertial frame s and s' have their axes paralell and pasitions of origin o' of s' relative to origin to s is given by ro=i+j+3k.what is the magnitude of position vector of a point p in s' if the co-ordinates p in s is(2,3,4)
To find the magnitude of the position vector of point P in frame S', we need to perform a coordinate transformation using the given positions of the origins and the coordinates of point P in frame S.
Let's break down the given information:
- The position vector of point O' in frame S relative to the origin O of frame S is given by ro = i + j + 3k.
The position vector of point P in frame S is given by p = (2, 3, 4).
Now, let's go step by step to find the position vector of point P in frame S':
1. Calculate the position vector of point P in frame S' relative to the origin O':
To do this, we need to subtract the position of origin O' of frame S' relative to the origin O of frame S.
Position vector of point P in frame S' relative to O' is given by p' = p - ro.
Substituting the given values, we have:
p' = (2, 3, 4) - (1, 1, 3) = (1, 2, 1)
So, the position vector of point P in frame S' relative to O' is p' = (1, 2, 1).
2. Calculate the magnitude of the position vector of point P in frame S':
The magnitude of a vector is calculated using the formula:
|V| = sqrt(Vx^2 + Vy^2 + Vz^2),
where Vx, Vy, and Vz are the components of the vector.
For our position vector p' = (1, 2, 1), the magnitude is:
|p'| = sqrt(1^2 + 2^2 + 1^2) = sqrt(6).
Therefore, the magnitude of the position vector of point P in frame S' is sqrt(6).