Vector u is represented by the directed line segment RS and vector v is represented by the directed line segment OP. If R=(8,-2), S=(11,-6), O=(-3,-9), and P=(0,-13), are u and v equal? Explain how you reached your answer.
they are equal because their directions and magnitudes are equal.
The line segments have equal slopes and lengths.
To determine if vectors u and v are equal, we need to check if their components (x and y) are equal.
Given that vector u is represented by the directed line segment RS and vector v is represented by the directed line segment OP, we can find the components of u and v as follows:
The components of vector u can be calculated as:
u = (x2 - x1, y2 - y1)
u = (11 - 8, -6 - (-2))
u = (3, -4)
The components of vector v can be calculated as:
v = (x2 - x1, y2 - y1)
v = (0 - (-3), -13 - (-9))
v = (3, -4)
Comparing the components of u and v, we see that they are both (3, -4).
Therefore, since the components of u and v are equal, we can conclude that vectors u and v are equal.
To determine if vector u and vector v are equal, we need to check if their corresponding components are equal.
First, let's find the components of vector u. The components of u are given by the difference in the x-coordinates and the difference in the y-coordinates of points R and S.
x-component of u = x-coordinate of S - x-coordinate of R = 11 - 8 = 3
y-component of u = y-coordinate of S - y-coordinate of R = -6 - (-2) = -4
So, vector u = (3, -4).
Similarly, let's find the components of vector v. The components of v are given by the difference in the x-coordinates and the difference in the y-coordinates of points O and P.
x-component of v = x-coordinate of P - x-coordinate of O = 0 - (-3) = 3
y-component of v = y-coordinate of P - y-coordinate of O = -13 - (-9) = -4
So, vector v = (3, -4).
Comparing the components of vector u and vector v, we can see that both the x-components and the y-components are equal. Therefore, u and v are equal.
To summarize, vector u and vector v are equal because their corresponding components are equal. Vector u = (3, -4) and vector v = (3, -4).