Question

What will be the maximum number of rectangular components into which a vector can be split in its own plane?
$\begin{align}
  & A.2 \\
 & B.3 \\
 & C.4 \\
 & D.\infty \\
\end{align}$

Answer 1

Hint: The rectangular components of the vector are the parts of a vector into which a vector gets resolved. Basically, these are in horizontal and vertical directions. The rectangular components will be perpendicular to each other also. Hope these all may help you to solve this question.

Complete step-by-step solution:
In a planar condition or a two-dimensional configuration, we will be moving either in a horizontal direction or vertical direction or both can also be possible. Let us assume a situation for example. Suppose you are going upstairs. When we move or go upstairs we will be having two kinds of motion. One is in the upward direction and the other is in the forward direction. The vertically upward motion can be considered as the motion in the y-axis. This will be the vertical component of the vector. While going upstairs you will be moving horizontally forwards which is considered as in x-axis. Thus your horizontal motion will be the horizontal component of actual motion. In short, we can say that our motion is resolved into two components. No more other components can be made in this 2D motion.
$y-component=a\sin \theta $
$x-component=a\cos \theta $

Therefore, the correct answer for the question has been obtained. it is given as option A.

Note:

The resultant of the vector will be the square root of the sum of squares of each of the components of a vector. Let the vector be given as$\vec{A}$. Therefore the results of the magnitude of the vector when it is resolved into components will be given as,
$\left| {\vec{A}} \right|=\sqrt{{{\left( A\sin \theta \right)}^{2}}+{{\left( A\cos \theta \right)}^{2}}}$
And the angle between the component and the resultant vector will be,
$\tan \theta =\dfrac{{{A}_{y}}}{{{A}_{x}}}$.