How to Find Vector Components Along an Axis

AI Thread Summary
To find the vector components along an axis, start by determining the components of each vector using trigonometric functions. For Vector A, with a magnitude of 3 m at a 10-degree angle, Ax is calculated as 3*cos(10) and Ay as 3*sin(10). Vector B, directed along the negative x-axis with a magnitude of 10 m, has a y-component of zero (By = 0) and Bx as -10 m. To solve for the resultant vectors A + B and A - B, sum the respective x and y components. Understanding that the y-component of Vector B is zero simplifies the calculations significantly.
anti404
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1. Vector A has a magnitude of 3 m and makes an angle of 10o with the positive x axis. Vector B also has a magnitude of 10 m and is directed along the negative x axis. Enter your answers in distance then angle(in degrees).
Find A + B
Find A - B




2. R = sqrroot(Cx^2+Cy^2)
Cx = Ax+Bx
Cy = Ay+By
A*sin(theta)=x
B*sin(theta)=y




3. 3*sin10=.5209 = Ay; 3*cos10=2.954=Ax

basically, I don't know how to get By and Bx values from a vector that is following either axis. if I could get those, then I would become unstuck from this problem very quickly. any conceptual help would be appreciated.
Justin
 
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anti404 said:
1. Vector A has a magnitude of 3 m and makes an angle of 10o with the positive x axis. Vector B also has a magnitude of 10 m and is directed along the negative x axis. Enter your answers in distance then angle(in degrees).
Find A + B
Find A - B




2. R = sqrroot(Cx^2+Cy^2)
Cx = Ax+Bx
Cy = Ay+By
A*sin(theta)=x
B*sin(theta)=y




3. 3*sin10=.5209 = Ay; 3*cos10=2.954=Ax

basically, I don't know how to get By and Bx values from a vector that is following either axis. if I could get those, then I would become unstuck from this problem very quickly. any conceptual help would be appreciated.
Justin

Just draw out the B vector on its own. The Bx and By components have to add up to the total B vector. If the vector is ONLY in the x direction, what do you think the y component would be?
 
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