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?

Because the ramps run parallel in the same direction, their vectors point the same way, so the scalar is positive. The shorter ramp is 30 feet compared with the first ramp’s 50 feet, giving a scale factor of 30/50 = 0.6, which is between 0 and 1. Therefore, the scalar is less than 1 but positive.

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