Question

Two vectors are said to be parallel if they point in the same direction or if they point in opposite directions. Part A Are these two vectors parallel? Show your work and explain. Part B Are these two vectors parallel? Show your work and explain.

Answer 1

Answer:

Knowing that those vectors start at the point (0,0) we can "think" them as lines.

As you may know, two lines are parallel if the slope is the same, then we can find the "slope" of the vectors and see if it is the same.

A) the vectors are: (√3, 1) and (-√3, -1)

You may remember that the way to find the slope of a line that passes through the points (x1, y1) and (x2, y2) is s = (y2 - y1)/(x2 - x1)

Because we know that our vectors also pass through the point (0,0)

then the slopes are:

 (√3, 1) -----> s = (1/√3)

 (-√3, -1)----> s = (-1/-√3) =  (1/√3)

The slope is the same, so the vectors are parallel.

Part B:

The vectors are: (2, 3) and (-3, -2)

the slopes are:

(2, 3) -----> s = 3/2

(-3, -2)----> s = -2/-3 = 2/3

the slopes are different, so the vectors are not parallel.