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

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

What is the direction of vector A + vector B?

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Answer 1 · 2018-02-04T01:55:09

$- {63.425}^{o}$ $-63.425^o$

Explanation:

Made 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:

$A + B = 2 i - 4 j$ $A+B=2i-4j$

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. $2.0 i$ $2.0i$ and $- 4.0 j$ $-4.0j$ 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:

$tan θ = \frac{O p p}{A d j} \Rightarrow θ = {tan}^{- 1} (\frac{O p p}{A d j})$ $tantheta = (Opp) /( Adj) implies theta=tan^-1((Opp) /(Adj))$

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

$θ = {tan}^{- 1} (\frac{4.0}{2.0}) = {63.425}^{o}$ $theta = tan^-1(4.0/2.0)=63.425^o$

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

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

$\to 360 - 63.425 = {296.565}^{o}$ $-> 360-63.425=296.565^o$

Answer 2 · 2018-02-04T02:19:13

e. ${296.5}^{\circ}$ $296.5^@$
f. $0^{\circ}$ $0^@$

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 $90^{\circ}$ $90^@$ and the minus y axis is at $270^{\circ}$ $270^@$ . Ref:
http://chortle.ccsu.edu/VectorLessons/vch05/vch05_3.html

e. From your work, $\to A + \to B = 2 cm ˆ i - 4 cm ˆ j$ $vec(A) + vec(B) = 2 " cm " hati - 4 " cm " hatj$ . That puts the vector in the 4th quadrant. Draw the vector with the arrowhead at x=2, y=-4.

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

${tan}^{- 1} (\frac{2}{4}) = {26.5}^{\circ}$ $tan^-1(2/4) = 26.5^@$

The -y axis is already $270^{\circ}$ $270^@$ counterclockwise from the +x axis, so the answer to e is $270^{\circ} + {26.5}^{\circ} = {296.5}^{\circ}$ $270^@+26.5^@ = 296.5^@$ .

f. From your work, $\to A - \to B = 4 cm ˆ i + 0 cm ˆ j$ $vec(A) - vec(B) = 4 " cm " hati + 0 " cm " hatj$ . Therefore the resultant lies along the x axis. That is an angle of $0^{\circ}$ $0^@$ .

I hope this helps,
Steve

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

What is the direction of vector A + vector B?

2 Answers

Explanation:

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