Question

Make vector A on the simulation have a magnitude of exactly 10 units. What were the starting points and ending points of your vector?

Answer 1

Answer:

Making a vertical vector, we have a starting point at (-5,2) and an end point at (5,2) that will give us a vector of magnitude of 10 units.

Explanation:

In order to make vectors that have a magnitude of 10 units, the distance between the starting and ending points must be equal to 10.

The easiest way is to set points on either an horizontal or vertical line to make horizontal or vertical vectors.

We can have starting point at (-5,2) and  then move up 10 units so we will be at the ending point (5,2), thus the distance between them is 10 units so the vector has a magnitude of 10 units.

We can verify that using the formula for the magnitude which requires first to find the vector.

$\vec v = \text{End point } - \text{Start point}$

So for the points we have

$\vec v = (5,2)-(-5,2)$

We can work with each component, for the x component we have 5-(-5) which give us 10 and for the y component we have 2-2  which give us 0, so the vector is

$\vec v =$

Thus its magnitude is

$|v|= \sqrt{v_x^2+v_y^2}\\|v|= \sqrt{10^2+0^2}\\|v|=\sqrt{100}\\|v|=10$

Thus we have verified our vector has a length 10.