Question

Define rectangular components of vector.

Answer 1

1. Rectangular components of the vector are defined as the parts of a vector resolved into vertical and horizontal vectors.
2. Rectangular components are perpendicular to each other.
3. Let a vector $\overrightarrow{A}$ be resolved into two rectangular components $A_{x}and{A}_Y$ along the x-axis and y-axis resp.

4. If $\theta$ is the angle made by the vector $\overrightarrow{A}$ with an x-axis, then

$$\begin{gathered} A_x=A\cos \theta \\ and{A}_y=A\sin \theta \end{gathered}$$

5. Using the triangle law of vector addition, we can write $\overrightarrow{A=}{A}_xˆi+Ayˆj,whereˆiandˆjareunitcectorsalongxandyaxisresp.$

Thus $\overrightarrow{A=}A\cos \theta ˆi+A\sin {\theta }_{}ˆj,$