3. Vectors

If two velocity vectors are added using the component method, which of the following correctly describes how to find the magnitude of the resultant velocity vector $v_r$ given their components $v_{1x}$, $v_{1y}$, $v_{2x}$, and $v_{2y}$?

Given two vectors $A$ and $B$ with components $A=(3,4)$ and $B=(1,-2)$, what are the components of the vector $A+B$?

Given two vectors in a plane, how many distinct combinations (regardless of magnitude or direction) can sum to produce an arbitrary third vector?

Which of the following does not describe the process of adding vectors by components?

Suppose you have four vectors of equal magnitude: $\mathrm{Vector} A$ points along the positive $x$-axis, $\mathrm{Vector} B$ points along the positive $y$-axis, $\mathrm{Vector} C$ points at $45°$ above the $x$-axis (in the first quadrant), and $\mathrm{Vector} D$ points at $45°$ below the $x$-axis (in the fourth quadrant). Which pair of vectors, when added, will result in the largest positive $y$ component?

Given two vectors $A$ and $B$ with components $A=\left(3,4\right)$ and $B=\left(1,-,2\right)$, what is the single vector that represents $A+B$ when added by components?

Which of the following operations will not change a $\mathrm{vector}$?