Question

Select all the correct locations on the graph.

Vector u has its initial point at (5, -7) and its terminal point at (8, -9). On the graph, identify the scalar multiples of u that have a direction opposite that of u.

Answer 1

To find scalar multiples of vector u in the opposite direction, subtract the initial point from the terminal point. Multiply the resulting vector by any scalar to obtain scalar multiples in the opposite direction.

Step-by-step explanation:

In order to find the scalar multiples of vector, u, that have a direction opposite to u, we need to determine the opposite direction of u. To do this, we subtract the initial point from the terminal point of u. The initial point of u is (5, -7) and the terminal point is (8, -9). Subtracting the initial point from the terminal point gives us (8 - 5, -9 - (-7)) which simplifies to (3, -2). This is the vector representing the opposite direction of u.

To find scalar multiples of u in the opposite direction, we can multiply the vector (3, -2) by any scalar. This will give us a new vector with the same direction, but opposite in magnitude. For example, if we multiply (3, -2) by -1, we get (-3, 2) which is a scalar multiple of u in the opposite direction.