Vectors, magitude, scalar components

[brittbc]

Homework Statement

the displacement vector A has scalr omponents of Ax= 80.0 m and Ay= 60.0 m. the displacement vector B has a scalr component Bx= 60.0 m and a magnitude of B=75.0m. The displacement vecto C has a magnitude of C= 100.0 m and is directed at an angle of 36.9 degrees above the + x axis. Two of these vectors are equal. determine which two, and support your choice with a calculation.

Homework Equations

The Attempt at a Solution

vector A= 100m
By= 45m
vector A= vector C

 

[Kurdt]

So vector A and vector C have the same magnitude. Can you show they're both 36.9 degrees above the x-axis.

 

[thomate1]

The two vectors that are equal are A and C. This can be determined by calculating the magnitude of vector A using the Pythagorean theorem: A = √(Ax^2 + Ay^2) = √(80.0m^2 + 60.0m^2) = √(6400m^2 + 3600m^2) = √10000m^2 = 100m. This is the same magnitude as vector C, which is also 100m. Additionally, the angle of vector C, 36.9 degrees, is the same as the angle between the +x axis and vector A, making them equal in direction as well. Therefore, vector A and vector C are equal.