Question

Answer the following question about the distance vector 𝑥⃗={2.5𝑖⃗+5.4𝑗⃗}𝑚
a. What is magnitude of the distance vector?
b. What is the direction (angle) that the distance vector makes with the positive x-axis?
c. What vector when combined with the distance vector would give a resultant vector of 𝑥⃗={25𝑖⃗}𝑚?
3.

Answer 1

All i need help with is C

Answer 2

You have a vector \(\vec x=2.5~\vec{i}+5.4~\vec{j}\), and you're looking for some vector \(\vec y=a~\vec{i}+b~\vec{j}\) such that \(\vec x+\vec y=25~\vec i\).

Add the components together:
\[\vec x+\vec y=\color{red}{(2.5+a)}~\vec i+\color{blue}{(5.4+b)}~\vec j=\color{red}{25}~\vec i+\color{blue}{0}~\vec j\]