What Are Rectangular Scalar Components in Vector Analysis?

[sunbunny]

Hey,

In the question that I'm working on it says to resolve v1 and v2 into rectangular scalar components but i have no idea what a rectangular scalar component is and i can't find it in my textbook. if anyone could tell me what they are that would be very helpful!

thanks

 

[quasar987]

Say you have a vector [itex]\vec{v}[/itex]. It can be written as [itex]\vec{v}=(v_x,v_y)[/itex] or, using the unit vectors in the directions of the x-axis and y-axis, [itex]\hat{x}[/itex] and [itex]\hat{y}[/itex] (sometimes also noted [itex]\vec{i}[/itex] and [itex]\vec{j}[/itex]) as [itex]\vec{v}=v_x\hat{x}+v_y\hat{y}[/itex].

In either case, we call [itex]v_x[/itex] and [itex]v_y[/itex] the recatangular scalar components of [itex]\vec{v}[/itex].

Is it clear?

 

[sunbunny]

Yes, now it is clear, thank you for your help, i really appreciate it :)

 

[PhanthomJay]

Hey,

In the question that I'm working on it says to resolve v1 and v2 into rectangular scalar components but i have no idea what a rectangular scalar component is and i can't find it in my textbook. if anyone could tell me what they are that would be very helpful!

thanks

A rectangular scalar components of a vector in a 2D plane are the magnitude of the projection of the vector onto the x or y axis, respectively. Given a vector V that has a magnitude of V and that makes an angle [tex]\theta[/tex] with the x axis, then the scalar component of the vector along the x-axis is [tex] Vcos\theta[/tex], and the scalar component of the vector along the y-axis is [tex] Vsin\theta[/tex].

 

[sunbunny]

okay, thanks that helps a lot for trying to find the x and y components. thank you

 

[sunbunny]

z-axis components

Hey, I'm just wondering if i need to find scalar components for a magnitude on the z-axis, do i go about the same way i would with regual x,y compenents, or is there something else that i need to do??

Thanks!