Why Do My Vector Addition Calculations Differ from the Textbook's Answers?

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The user is struggling with vector addition calculations for their Grade 12 math homework, specifically with vectors A and B. They initially copied their teacher's method but found discrepancies between their results and the textbook answers. Key issues identified include incorrect calculations for the components of vector B and the unnecessary addition of 180 degrees to the angle, which misrepresented the vector's direction. After clarification, it was revealed that the textbook's answers were simply rounded differently, confirming the user's calculations were essentially correct. The discussion highlights the importance of careful component calculation and understanding vector direction.
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Homework Statement



Hi, for some reason I can't post my homework question (Grade 12 math)


How do i fix this?

Here's my homework question






Homework Statement



In Exercises 15-30, add the given vectors by using the trigonometric functions and the Pythagorean theorem

19. A = 9.821,θA = 34.27
B = 17.45,θB = 752.50

Homework Equations



R=√Rx2+Ry2=

θ=tan-1 Ry/Rx =

The Attempt at a Solution




So here's what I did. I copied exactly what my teacher did but, when I checked the answer at the back of the book, the answer was wrong =(. Can you guys point out how I'm not getting the correct answer? thanks.


Here's what I have so far

19.

x component y component

Ax= 9.821cos34.27 Ay=9.821sin34.27
= 8.116 =5.530

Bx=17.45cos752.50 By=17.45cos752.50
= 14.72 =14.72



=22.84 =20.25

R=√22.84(2) + 20.25(2)= 30.52


θ=tan-1 20.25/22.84=41.56

θ=180+41.56




EDIT IT SAYS IN THE BOOK THAT THE ANSWERS ARE

R=27.27, θ=33.14
 
Last edited:
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Why have you added 180 degrees to your angle?

Note that BOTH of your vectors lie in the first quadrant, so their sum must lie there as well.
 
arildno said:
Why have you added 180 degrees to your angle?

Note that BOTH of your vectors lie in the first quadrant, so their sum must lie there as well.

?

I don't get it =(
 
Last chance U said:
?

I don't get it =(

Both of your given vectors point to the northeast, so their sum must also point to the northeast. When you added 180 degrees to the angle you forced your vector to point to the southwest. Why would you do that?
 
Last chance U said:

Homework Statement



Hi, for some reason I can't post my homework question (Grade 12 math)


How do i fix this?

Here's my homework question






Homework Statement



In Exercises 15-30, add the given vectors by using the trigonometric functions and the Pythagorean theorem

19. A = 9.821,θA = 34.27
B = 17.45,θB = 752.50

Homework Equations



R=√Rx2+Ry2=

θ=tan-1 Ry/Rx =

The Attempt at a Solution




So here's what I did. I copied exactly what my teacher did but, when I checked the answer at the back of the book, the answer was wrong =(. Can you guys point out how I'm not getting the correct answer? thanks.


Here's what I have so far

19.

x component y component

Ax= 9.821cos34.27 Ay=9.821sin34.27
= 8.116 =5.530

Bx=17.45cos752.50 By=17.45cos752.50
= 14.72 =14.72
Your components for ##\vec{B}## are wrong. They shouldn't be equal.

=22.84 =20.25

R=√22.84(2) + 20.25(2)= 30.52


θ=tan-1 20.25/22.84=41.56

θ=180+41.56
Even with your incorrect numbers, both components of ##\vec{R}## are positive, so you should expect the angle to be between 0° and 90°, which is what you got from the arctangent function. So why did you add 180° to your result?

EDIT IT SAYS IN THE BOOK THAT THE ANSWERS ARE

R=27.27, θ=33.14
 
Update guys, I have actually had the right the answer the whole time rofl. The book just rounded it differently lol. Thanks for the help though.