What is the Resolution of a vector into two perpendicular components?

Resolution of a vector is the process of splitting up a vector (force) into two perpendicular component parts. They are called rectangular components because the two component forces are mutually perpendicular.

At an angle θ with x axis, the force R acts at a point O. R can be resolved into two rectangular components along x and y axis. Two perpendicular lines CQ and CP are drawn to x and y axis. In the right angled triangle OQC,

Cos θ = OQ / OC

OQ = OC Cos θ

we know that  OC = R

OQ= R Cos θ

Therefore the horizontal component of the force R is R cosƟ.

In the right angled triangle OPC,

Cos (90-Ɵ) = OP / OC

SinƟ = OP / OC ——– Cos (90-Ɵ) = SinƟ

OP = OC SinƟ

we know that  OC = R

OP = R SinƟ

The vertical component of the force R is R sinƟ