Resolution of Vectors :
If `vec P +vec Q=vec R` , the resultant then conversely `vec R = vec P + vec Q` i.e. the vector `vec R` can be split up so that the vector sum of the split parts equals the original vector `vec R`. If the split parts are mutually perpendicular then they are known as components
of `vecR` and this process is known as resolution. The orthogonal component of any vector along another direction which is at an angular separation q is the product of the magnitude of the vector and cosine of the angle between them `( q )`. Therefore the component of `vec A` is `A cos q` .
Note: In physics, resolution gives unique and mutually independent components only if the resolved components are mutually perpendicular to each other. Such a resolution is known as rectangular or orthogonal resolution and the components are called rectangular or orthogonal components.
` O`-the origin, `OP` - the given vector `vec V`
`PP_x` - perpendicular to `X` axis.
`PP_y`- Perpendicular to `Y` axis.
`vec (OP)_x + vec (P_xP) = vec (OP) = vec V`
`vec V = vec V_x+ vec V_y`
`V_x = V cosq` & `V_y = V sin q`
Unit vector along the direction of `vec A` is `vec A = vec A//A`, Where `A` is magnitude of `vec A`. `hat i,hat j, hat k`, are the unit vectors along positive direction of `X, Y` and `Z` axis respectively, then the rectangular resolution of vector `vec A` can be represented.
`vec A= A_x hat i+ A_yhat j + A_z hat k` where `A_x, A_y, A_z` are the magnitudes of `X, Y` and `Z ` components of `vec A`. The magnitude of vector `vec A` is given by `|vec A| = sqrt(A_x^2 +A_y^2 +A_z^2)`.
of `vecR` and this process is known as resolution. The orthogonal component of any vector along another direction which is at an angular separation q is the product of the magnitude of the vector and cosine of the angle between them `( q )`. Therefore the component of `vec A` is `A cos q` .
Note: In physics, resolution gives unique and mutually independent components only if the resolved components are mutually perpendicular to each other. Such a resolution is known as rectangular or orthogonal resolution and the components are called rectangular or orthogonal components.
` O`-the origin, `OP` - the given vector `vec V`
`PP_x` - perpendicular to `X` axis.
`PP_y`- Perpendicular to `Y` axis.
`vec (OP)_x + vec (P_xP) = vec (OP) = vec V`
`vec V = vec V_x+ vec V_y`
`V_x = V cosq` & `V_y = V sin q`
Unit vector along the direction of `vec A` is `vec A = vec A//A`, Where `A` is magnitude of `vec A`. `hat i,hat j, hat k`, are the unit vectors along positive direction of `X, Y` and `Z` axis respectively, then the rectangular resolution of vector `vec A` can be represented.
`vec A= A_x hat i+ A_yhat j + A_z hat k` where `A_x, A_y, A_z` are the magnitudes of `X, Y` and `Z ` components of `vec A`. The magnitude of vector `vec A` is given by `|vec A| = sqrt(A_x^2 +A_y^2 +A_z^2)`.