Vectors Please Help ( What is the direction of vector A + vector B?)

What is the direction of vector A + vector B?enter image source here

2 Answers
Feb 4, 2018

63.425o

Explanation:

Made on Microsoft PaintMade on Microsoft Paint

Not drawn to scale

Sorry for the crudely drawn diagram but I hope it helps us see the situation better.

As you have worked out earlier in the question the vector:

A+B=2i4j

in centimeters. To get the direction from the x-axis we need the angle. If we draw the vector and split it up into its components, i.e. 2.0i and 4.0j you see we get a right angled triangle so the angle can be worked out using simple trigonometry. We have the opposite and the adjacent sides. From trigonometry:

tanθ=OppAdjθ=tan1(OppAdj)

In our case the side opposite the angle is 4.0cm so 4.0cm and the adjacent side is: 2.0cm so:

θ=tan1(4.02.0)=63.425o

Obviously this is anti-clockwise so we must put a minus in front of the angle 63.425

If the question is asking for the positive angle going clockwise around the diagram then simple subtract this from 360o

36063.425=296.565o

Feb 4, 2018

e. 296.5
f. 0

Explanation:

It looks like your answer for e is wrong and perhaps you have not found an answer for f. So I will help with both.

Note: I am using the angle measuring method in which you start at the +x axis and circulate counterclockwise to the vector. So the +y axis is at 90 and the minus y axis is at 270. Ref:
http://chortle.ccsu.edu/VectorLessons/vch05/vch05_3.html

e. From your work, A+B=2 cm ˆi4 cm ˆj. That puts the vector in the 4th quadrant. Draw the vector with the arrowhead at x=2, y=-4.

Let's calculate the angle θe between the -y axis and the vector. The length of the side opposite is 2 cm and the side adjacent is 4 cm.

tan1(24)=26.5

The -y axis is already 270 counterclockwise from the +x axis, so the answer to e is 270+26.5=296.5.

f. From your work, AB=4 cm ˆi+0 cm ˆj. Therefore the resultant lies along the x axis. That is an angle of 0.

I hope this helps,
Steve