Question

Under what circumstances would a vector have components that are equal in magnitude?

Answer 1

Answer:

In case of rectangular components the magnitude of two components will be equal if the vector makes 45° with +x-axis.

Step-by-step explanation:

In case of rectangular components, the magnitude of the two components will be equal if the vector makes an angle of 45° with +x-axis.

Mathematically it could be seen as:

Let $A_x$ and $A_y$ be the x and y components of a vector then it is given as:

The x-component of the vector is calculated as:

$A_{x}=A \cos45\degree=\dfrac{A}{\sqrt{2}}$

Similarly the y-component of the vector is calculated as:

$A_{y}=A \sin45\degree=\dfrac{A}{\sqrt{2}}$

Hence, we get that $A_{x}=A_{y}$