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?
a scalar less than -1
a scalar between -1 and 0
a scalar between 0 and 1
a scalar greater than 1

Explanation:

Step1: Understand vector - scalar relationship

When two vectors are parallel, the shorter vector can be obtained by multiplying the longer vector by a positive scalar less than 1 if they have the same direction.

Step2: Analyze ramp lengths

The first ramp is 50 feet long and the second (shorter) ramp is 30 feet long. Since they are parallel, to get the vector of the 30 - foot ramp from the 50 - foot ramp vector, we multiply by $\frac{30}{50}=0.6$ which is between 0 and 1.

Answer:

C. a scalar between 0 and 1