Question

A ramp is 50 feet long and has a 6° incline. a second ramp is 30 feet long and runs parallel to the first ramp. to determine the vector representing the shorter ramp, what scalar must be multiplied to the vector representing the first ramp?

1. To determine the vector representing the shorter ramp, we must multiply the vector representing the first ramp by a scalar, whose value lies between 0 and 1.

### What are scalars?

These are the quantities that only have magnitude.

### What are vectors?

These are the quantities that have both magnitude and direction.
Given:
• First ramp is 50 feet long and has a 6° incline.
• Second ramp is 30 feet long and runs parallel to the first ramp.
From this, we can observe that the magnitude of the first ramp is greater than that of the second ramp. Because of a smaller magnitude, in order to obtain a vector for the second ramp from the first ramp, we will multiply a scalar value, ranging from 0 to 1 with the vector of the first ramp.
Hence, to determine the vector representing the shorter ramp, we must multiply the vector representing the first ramp by a scalar between 0 and 1.