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 $\vec{v}$. It can be written as $\vec{v}=(v_x,v_y)$ or, using the unit vectors in the directions of the x-axis and y-axis, $\hat{x}$ and $\hat{y}$ (sometimes also noted $\vec{i}$ and $\vec{j}$) as $\vec{v}=v_x\hat{x}+v_y\hat{y}$.

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

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 $$\theta$$ with the x axis, then the scalar component of the vector along the x-axis is $$Vcos\theta$$, and the scalar component of the vector along the y-axis is $$Vsin\theta$$.

 

[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!