Find the angle (round to the nearest degree) between the vectors.
< -7, -28 > and < -6, -22 >

Question

Find the angle (round to the nearest degree) between the vectors. < -7, -28 > and < -6, -22 > A) 1° B) 89° C) 658 D) no solution

Quizplus · Accepted Answer

The angle θ between two vectors A = and B = can be found using the dot product formula: A·B = |A||B|cos(θ), where |A| and |B| are the magnitudes of vectors A and B, respectively. The dot product A·B = a1*b1 + a2*b2, and the magnitudes |A| = sqrt(a1^2 + a2^2) and |B| = sqrt(b1^2 + b2^2).For vectors A = < -7, -28 > and B = < -6, -22 >:- The dot product A·B = (-7)*(-6) + (-28)*(-22) = 42 + 616 = 658.- The magnitude of A = sqrt((-7)^2 + (-28)^2) = sqrt(49 + 784) = sqrt(833).- The magnitude of B = sqrt((-6)^2 + (-22)^2) = sqrt(36 + 484) = sqrt(520).Thus, cos(θ) = 658 / (sqrt(833) * sqrt(520)).Calculating the angle θ gives a value very close to 1° when rounded to the nearest degree.

Find the Angle (Round to the Nearest Degree) Between the Vectors