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

We can first find the magnitudes of the vectors using the Pythagorean theorem: |A| = sqrt((A_x)^2 + (A_y)^2) = sqrt(16 + 10.24) = sqrt(26.24) |B| = sqrt((B_x)^2 + (B_y)^2) = sqrt(6.25 + 30.25) = sqrt(36.5) Then, we can find the dot product of the two vectors: A · B = (A_x)(B_x) + (A_y)(B_y) = (4)(2.5) + (3.2)(5.5) = 8.8 + 17.6 = 26.4 Using the formula for the dot product of two vectors, we get: A · B = |A||B| cos(θ) 26.4 = sqrt(26.24) sqrt(36.5) cos(θ) cos(θ) = 26.4 / (sqrt(26.24) sqrt(36.5)) θ = arccos(0.896) = 27.1º Therefore, the answer is C) 27º.

Vector Has Components Ax = +4

Vector Has Components A_x = +4