What is the Direction of the Vector with Given Components?

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Homework Help Overview

The discussion revolves around determining the direction of a vector given its x and y components, specifically with an x component of -25.0 units and a y component of 40.0 units. The original poster attempts to calculate both the magnitude and direction of the vector, noting a discrepancy between their result and the textbook answer.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of the vector's magnitude and direction, with the original poster expressing confusion over the textbook's answer of 58 degrees. Some participants question the assumptions made regarding the quadrant in which the vector lies and the implications of the signs of the components.

Discussion Status

There is an ongoing exploration of the problem, with some participants suggesting that the textbook may be incorrect. The conversation includes inquiries about the specific wording of the textbook's direction and whether it aligns with the calculated angle.

Contextual Notes

Participants note that the textbook does not specify the direction beyond providing the angle of 58 degrees, leading to further questioning of the assumptions regarding the vector's orientation.

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Homework Statement



A vector has x component of (-25.0) units and y component of (40.0) units. Find the magnitude and direction of this vector.

Homework Equations





The Attempt at a Solution



Magnitude = [tex]\sqrt{}(-25.0)^2+(40.0)^2[/tex]
= 47.17 units.

Direction = tan x = | 40.0 | / |-25.0|
= 1.6
x = tan^-1 (1.6)
= 58
since the vector is located in the IInd Quadrant theta = 180 -58 = 122 degrees.

But textbook answer is 58 degrees. I couldn't get it :confused:

Any suggestions ?? Thank you...
 
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hi thushanthan! :wink:
thushanthan said:
A vector has x component of (-25.0) units and y component of (40.0) units. Find the magnitude and direction of this vector.

But textbook answer is 58 degrees. I couldn't get it :confused:

Any suggestions ?? Thank you...

(which book is it?)

you're right, the text-book is wrong :smile:

(as you know, if the direction was 58º, both x and y would be positive)
 
Thank you :smile:
 
What, exactly, did your textbook say? Anything like "58 degrees west of north" or "north 58 degrees west"?
 
No there is no direction mentioned. Only the value of theta is given, which is 58 degrees. :frown:
 
It's painful when the textbook is wrong and you've spent hours on one question you KNOW you did correctly... but there is some sense of victory when you find out they are wrong and you are right :)
 

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