• Jan 20th 2011, 01:54 PM
nautica17
This is a problem from my calculus 3 class.

"Find the component forms of v + w and v - w in 2-space, given that ||v|| = 1, ||w|| = 1, v makes an angle of pi/6 with the positive x-axis, and w makes an angle of 3pi/4 with the positive x-axis."

Okay, so I think have the answer but I want to be a hundred percent certain.

Looking at the unit circle.. I get these values for the components based on the angles given.
v = <sqrt(3)/2, 1/2>
w = <-sqrt(2)/2, sqrt(2)/2>

And so...
v + w = < ( sqrt(3)/2 + (-sqrt(2)/2) ), ( 1/2 + sqrt(2)/2 ) >
= < ( (sqrt(3) - sqrt(2)) / 2 ), ( (1 + sqrt(2)) / 2 ) >

v - w = < ( sqrt(3)/2 - (-sqrt(2)/2) ), ( 1/2 - sqrt(2)/2 ) >
= < ( (sqrt(3) + sqrt(2)) / 2 ), ( (1 - sqrt(2)) / 2 ) >

Am I doing it right?
• Jan 20th 2011, 02:04 PM
Plato
Quote:

Originally Posted by nautica17
"Find the component forms of v + w and v - w in 2-space, given that ||v|| = 1, ||w|| = 1, v makes an angle of pi/6 with the positive x-axis, and w makes an angle of 3pi/4 with the positive x-axis."
v = <sqrt(3)/2, 1/2>
w = <-sqrt(2)/2, sqrt(2)/2>
And so...
v + w = < ( sqrt(3)/2 + (-sqrt(2)/2) ), ( 1/2 + sqrt(2)/2 ) >
= < ( (sqrt(3) - sqrt(2)) / 2 ), ( (1 + sqrt(2)) / 2 ) >

v - w = < ( sqrt(3)/2 - (-sqrt(2)/2) ), ( 1/2 - sqrt(2)/2 ) >
= < ( (sqrt(3) + sqrt(2)) / 2 ), ( (1 - sqrt(2)) / 2 ) >
Am I doing it right?

Yes you are.
• Jan 20th 2011, 02:08 PM
nautica17
Cool, thanks! :)