Question

Two vectors, X and Y, form a right angle. Vector X is 48 inches long and vector Y is 14 inches long. The length of the

Answer 1

Answer:

$\left \| \vec R \right \|=50\ inches$

Explanation:

Vectors In The Plane

Given two vectors $\vec X$ and $\vec Y$, their sum is shown as the vector $\vec R$ in the image below. It can be seen the magnitude of R is the hypotenuse of a right triangle. i.e.

$\left \| \vec R \right \|=\sqrt{\left \| X \right \|^2+\left \| Y \right \|^2}$

The magnitude of $\vec X$ is 48 inches and the magnitude of $\vec Y$ is 14 inches, the magnitude of R is

$\left \| \vec R \right \|=\sqrt{48^2+14^2}$

$\left \| \vec R \right \|=\sqrt{2304+196}=\sqrt{2500}$

$\left \| \vec R \right \|=50\ inches$