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

-63.425^o

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=2i-4j

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:

tantheta = (Opp) /( Adj) implies theta=tan^-1((Opp) /(Adj))

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

theta = tan^-1(4.0/2.0)=63.425^o

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 360^o

-> 360-63.425=296.565^o

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, vec(A) + vec(B) = 2 " cm " hati - 4 " cm " hatj. That puts the vector in the 4th quadrant. Draw the vector with the arrowhead at x=2, y=-4.

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

tan^-1(2/4) = 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, vec(A) - vec(B) = 4 " cm " hati + 0 " cm " hatj. Therefore the resultant lies along the x axis. That is an angle of 0^@.

I hope this helps,
Steve