What do you mean by rectangular components of vector? Explain how a vector can be resolved into two rectangular components, in a plane.

Explanation

A vectoris resolved irrsuchraway that components obtained or resolutionare perpendicularto one: another: Components, so obtained, are known as: rectangular components. of vector:
Rectangular components of a vector in a plane
Leta vector `vec A` is resolved along X-axis and Y-axis. Taking the initial point of `vec A` as the origirco, O draw two axis. OX and OY `bot` to each other. From the head. of `vec A` draw. `PM bot OX and PN bot OY.` According to parallelogram law of vector addition
`vec (OP) = vec (OM) + vec (PM) [because vec (PM) = vec (ON)]`
`vec (OP) = vec (OM) + vec (ON) , implies vec A = vec A _(x) + vec A _(y)`
Now `vec A _(x) = A _(x ) hati implies vec A _(y) = A _(y) hatj`
Here `A _(x) = A cos theta implies A _(y) = A sin theta `
`implies A = sqrt ( A _(x) ^(2) + A _(y) ^(2))`
`tan theta = ( A _(y))/( A _(x)) implies theta = tan ^(-1) ((A _(y))/( A _(x))).`