
#1
Feb1314, 01:36 PM

P: 60

Hi everyone,
Just wanna know how does the the unit vector become in that form: [itex]\vec{n}=\frac{2x\vec{i}+2y\vec{j}}{\sqrt{(2x)^{2}+(2y)^{2}}}=\frac{x \vec{i}+y \vec{j}}{4}[/itex] 



#2
Feb1314, 02:54 PM

P: 498

Check your definition of "unit vector."




#3
Feb1314, 04:05 PM

P: 60

As far as I know, the unit vector or the normal vector is the vector divided by its magnitude.
But that's not what I need to know, what I need to know is the manipulation that occurred. [itex]\vec{n}=\frac{2x\vec{i}+2y\vec{j}}{\sqrt{(2x)^{2}+(2y)^{2}}}=\frac{2(x \vec{i}+y\vec{j})}{\sqrt{4(x^{2}+y^{2}})}=\frac{2(x \vec{i}+y\vec{j})}{2\sqrt{(x^{2}+y^{2}})}=\frac{x \vec{i}+y\vec{j}}{\sqrt{x^{2}+y^{2}}}[/itex] That's my best. :Z 



#4
Feb1314, 04:09 PM

Sci Advisor
P: 5,942

Unit Vector 



#5
Feb1314, 04:44 PM

P: 60

But how did it end up like this form: [itex]\frac{x \vec{i}+y \vec{j}}{4}[/itex]
And I've found something similar in Thomas Calculus: Is [itex]y^{2} + z^{2}[/itex] equal to 1 or something? much like [itex]sin^{2}\theta + cos^{2}\theta = 1 [/itex] 



#6
Feb1314, 06:01 PM

P: 498

You're looking for "the" unit normal vector. Normal to what?




#7
Feb1414, 03:35 AM

P: 60

Normal to the surface [itex]2x+3y+6z=12[/itex]




#8
Feb1414, 06:40 AM

P: 498

Okay, but clearly that isn't where the gradient in the original post came from. So if you want to know what happened in post #3 (why x^{2} + y^{2} = 1) then you need to state the original problem.




#9
Feb1414, 07:41 AM

P: 60

Sorry, that's not the correct surface, but the surface is [itex]x^{2}+y^{2}=16[/itex].
But I think I've got the idea: [itex]\vec{n}=\frac{x\vec{i}+y \vec{j}}{\sqrt{x^{2}+y^{2}}}=\frac{x\vec{i}+y\vec{j}}{\sqrt{16}}=\frac{ x\vec{i}+y\vec{j}}{4}[/itex] right? 



#10
Feb1414, 08:06 AM

P: 498




Register to reply 
Related Discussions  
Dot product of a vector with the derivative of its unit vector  Calculus & Beyond Homework  7  
How do you find the coordinate of a vector with the unit vector?  Linear & Abstract Algebra  1  
Ev(Unit Vector) and projection of a vector in a dot product  Calculus  1  
How do I calculate the binormal vector without using the principal unit normal vector  Calculus & Beyond Homework  1  
Symbolic represenation of the unit vector and the vector  General Math  11 