A vector `vec C` when added to the resultant of the vectors `vec A = 3 hati -4 hat j + 5 hat k` and vec B = 2 vec 2 hat I + 3 hat j -4 hat k` giv es a unit vector along y-axis. Find the magnitude of `vec C`.

Explanation

Resultant of `vec A and vec B` is
`vec R =vec A + vec B =(3 hat I -4 hat j +5 hat k) + (2 hat I +3 hat j -4 hat k)`
`=5 hat I -hat j + hat k`
Unit vector along y-axis `= hat j`
As per question ,brgt `vec C + vec R =hat j or vec C = hat j - v ec R = vec j -(5 vec i - vec j + vec k)`
`=- 5 vec i + 2 vec j - vec k`
`| vec C| = sqrt ((-5) ^(2) +(2) ^(2) +(-1) ^(2) (-1)^(2)) =sqrt 30` .