Question

Which pair of vectors could produce a resultant of 35?

A. <12,15>and <5,24>
B. (8,15) and (7,24)
C. (10,24)and (6,18)
D. (20,10) and (15,20)

Answer 1

The pair of vectors that could produce a resultant of 35 is option B, (8, 15).

Step-by-step explanation:

To find the pair of vectors that could produce a resultant of 35, we need to calculate the magnitude of each pair. The formula to calculate the magnitude of a resultant vector is: magnitude = sqrt(x^2 + y^2), where (x, y) are the components of the vector.

Let's calculate the magnitudes of each pair:

A. <12, 15>: magnitude = sqrt(12^2 + 15^2) = sqrt(144 + 225) = sqrt(369) ≈ 19.2

B. (8, 15): magnitude = sqrt(8^2 + 15^2) = sqrt(64 + 225) = sqrt(289) = 17

C. (10, 24): magnitude = sqrt(10^2 + 24^2) = sqrt(100 + 576) = sqrt(676) = 26

D. (20, 10): magnitude = sqrt(20^2 + 10^2) = sqrt(400 + 100) = sqrt(500) ≈ 22.4

Based on the calculations, the pair of vectors that could produce a resultant of 35 is option B, (8, 15).