If vector $c$ has a magnitude of $28.2$ units and points in the positive $x$-direction, which of the following correctly represents vector $c$ in component form?

Given six vectors labeled $\overrightarrow{a}$ through $\overrightarrow{f}$ with various magnitudes and directions as shown in Figure 1, which of the following statements is true about the sum of two vectors resulting in the greatest possible displacement from the origin?

If vector $a$ has an x-component of $3$ and vector $b$ has an x-component of $-2$, what is the sum of the x components of vectors $a$ and $b$?

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are vectors, what is the magnitude of $\overrightarrow{b}-3\overrightarrow{a}$ in terms of the magnitudes of $\overrightarrow{a}$ and $\overrightarrow{b}$, assuming they are in the same direction?

A force of magnitude $10$ $N$ acts at an angle of $30°$ above the positive $x$-axis in the $xy$-plane. How can this force be expressed as a Cartesian vector?

A person walks $4$ km east and then $3$ km north. What is the magnitude of the resultant displacement from the starting point?

Which of the following best describes the direction of the vector field $f(x,y)$ = $\frac{yi-xj}{x^2+y^2}$ at any point (x, y) in the plane?