What is the Direction of the Vector with Given Components?

[thushanthan]

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 = $$\sqrt{}(-25.0)^2+(40.0)^2$$
= 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

Any suggestions ?? Thank you...

 

[tiny-tim]

hi thushanthan!

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

Any suggestions ?? Thank you...

(which book is it?)

you're right, the text-book is wrong …

(as you know, if the direction was 58º, both x and y would be positive)

 

[thushanthan]

Thank you

 

[HallsofIvy]

What, exactly, did your textbook say? Anything like "58 degrees west of north" or "north 58 degrees west"?

 

[thushanthan]

No there is no direction mentioned. Only the value of theta is given, which is 58 degrees.

 

[Shaybay92]

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 :)