The sum of the three vectors shown in figure is zero. Find the magnitudes of the vectors `vec(OB) and vec(OC)`.

Explanation

Take the axes as shown in the ure

The x-component of `vec(OA)=(OA)cos90^0=0`
The x-component of `vec(OB)=(OB)cos0^0 = OB.
The x-component of `vec(OC)=(OC) cos 135^0= - 1/sqrt(2) OC.`
Hence, the x-component of the resulstant
` OB- 1/sqrt2 OC.` ....i.
It is given that the resultant is zero and hence its x-component is also zero. From i.
`OB 1/sqrt2 OC` ...........ii
`The y-component of `vec(OA)=OA cos 180^0=-OA`
The y-component of `vecOB=OB cos 90^0=0`.
The y-component of `vec(OC)= OC cos 45^0 = 1/sqrt2 OC`.
` = 1/sqrt2 OC -OA` .....iii
As the resultant is zero so is its y-compoentn from iii,
` 1/sqrt2OC=OA, or OC = sqrt)A=5sqrt2m`
From i. `OB = 1/sqrt2 OC=5m`.