Vector has components A_x = +4.0 units and A_y = +3.2 units,whereas vector has components B_x = +2.5 units and B_y = +5.5 units.The angle between the two vectors is A)24º B)65º C)27º D)39º E)14º

Question

Quizplus · Accepted Answer

First, we need to find the dot product of the two vectors: A_x * B_x + A_y * B_y = 4.0 * 2.5 + 3.2 * 5.5 = 15.2 Then, we can use the dot product formula to get the cosine of the angle between the two vectors: cos θ = (A_x * B_x + A_y * B_y) / (|A| * |B|) where |A| and |B| are the magnitudes of the two vectors. |A| = √(A_x^2 + A_y^2) = √(4.0^2 + 3.2^2) = 5 |B| = √(B_x^2 + B_y^2) = √(2.5^2 + 5.5^2) = 6 cos θ = 15.2 / (5 * 6) cos θ ≈ 0.507 Finally, we can use the inverse cosine function to get the angle between the two vectors: θ ≈ 60.8º Therefore, the closest answer choice is C, 27º.

Vector Has Components Ax = +4

Vector Has Components A_x = +4