Calculate the Angle (a + b) Makes with the x-axis for Vector (a + b)

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Homework Help Overview

The problem involves calculating the angle that the resultant vector (a + b) makes with the x-axis, given the coordinates of two vectors originating from the same point.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss calculating angles for individual vectors before considering the resultant vector. There is a suggestion to first add the vectors to find their components before determining the angle. Some participants express confusion about the subtraction of angles and the correct application of tangent functions.

Discussion Status

The discussion is ongoing, with various interpretations of how to approach the problem. Some participants have provided calculations for angles, while others question the methods used. There is no explicit consensus on the correct approach yet, but guidance has been offered regarding the need to add the vectors first.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is also a noted confusion regarding the application of tangent functions and angle calculations.

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Homework Statement



if vector :

line a starts from co-ordinates (0,0) and ends at (5,3)

line b starts from co-ordinates (0,0) and ends at (1,2)

what angle to the x-axis does the vector (a + b) make?

Homework Equations



tan ∅ = opposite / adjacent

The Attempt at a Solution



we can work out what angle a makes then what angle b makes.

then subtract angle b from a.

tan a = opposite / adjacent
tan a ^-1 (3/5) = a=30.964

tab b ^ (2/1) =b=63.435

b-a = 63.435-30.964
= 32.47 degrees

is this correct?
 
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No. You want to add the vectors first, then take the angle. What is the x component of a+b? What is the y component of a+b? Once you have these, then you can use the angle formula.
 
(5,3) + (1,2) = (6,5) is the vector of (a+b)

tan a = opposite / adjacent
tan a ^-1 (5/6) = a=39.806 degrees

tan x ^-1 (3/5) = x=30.964

angle of (a+b) = 8.842 degrees

is this correct
 
imy786 said:
(5,3) + (1,2) = (6,5) is the vector of (a+b)

This is fine. I'm not quite sure why you're still subtracting angles though.

tan(angle of a+b) = opposite/adjacent = ...

What's opposite? adjacent?
 
tan a = opposite / adjacent
tan a ^-1 (5/6) = a=39.806 degrees
 
imy786 said:
tan a = opposite / adjacent
tan a ^-1 (5/6) = a=39.806 degrees

This is the correct answer. Minor technicality though. You're taking the tangent of the angle of a+b, not the tangent of a.
 
tan ( a + B ) = opposite / adjacent
tan (a+b) ^-1 (5/6) =

angle of (a + b)=39.806 degrees

Thanks gb7nash
 
imy786 said:
tan (a+b) ^-1 (5/6) =
I have no idea what you mean by this.
 
Mark44 said:
I have no idea what you mean by this.

Good catch, I didn't even notice that.
 

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