Vector u is represented by the directed line segment Modifying above upper R upper S with right arrow and vector v is represented by the directed line segment Modifying above upper O upper P with right arrow. If upper R equals left parenthesis 8 comma negative 2 right parenthesis, upper S equals left parenthesis 11 comma negative 6 right parenthesis, upper O equals left parenthesis negative 3 comma negative 9 right parenthesis, and upper P equals left parenthesis 0 comma negative 13 right parenthesis, are u and v equal?

Question

Vector u is represented by the directed line segment Modifying above upper R upper S with right arrow and vector v is represented by the directed line segment Modifying above upper O upper P with right arrow. If upper R equals left parenthesis 8 comma negative 2 right parenthesis, upper S equals left parenthesis 11 comma negative 6 right parenthesis, upper O equals left parenthesis negative 3 comma negative 9 right parenthesis, and upper P equals left parenthesis 0 comma negative 13 right parenthesis, are u and v equal?

Answer 1

To determine if vectors u and v are equal, we need to calculate the vectors u and v using the given points and then compare the components.

Vector u = RS = (11 - 8, -6 - (-2)) = (3, -4)
Vector v = OP = (0 - (-3), -13 - (-9)) = (3, -4)

Comparing the components of u and v, we can see that they are equal. Therefore, vector u is equal to vector v.