Given vectors u=(-6,4) and v=(3.3) , determine if the vectors are orthogonal. If they are not orthogonal, find the angle between the two vectors. (1 point) Responses The vectors are orthogonal. The vectors are orthogonal. The vectors are not orthogonal. The angle between the two vectors is 72.5°. The vectors are not orthogonal. The angle between the two vectors is 72.5°. The vectors are not orthogonal. The angle between the two vectors is 101.3°. The vectors are not orthogonal. The angle between the two vectors is 101.3°. The vectors are not orthogonal. The angle between the two vectors is 130.6°.

Answer 1

To determine if the vectors are orthogonal, we can use the dot product formula.
The dot product of u and v is: u.v = (-6)(3) + (4)(3) = -18 + 12 = -6
Next, we find the magnitudes of the vectors:
|u| = √((-6)^2 + 4^2) = √(36 + 16) = √52
|v| = √(3^2 + 3^2) = √(9 + 9) = √18
To find the angle between the vectors, we can use the formula:
cosθ = u.v / (|u| * |v|)
cosθ = -6 / ( √52 * √18) = -6 / ( √936) = -6 / 30.6 ≈ -0.196
θ ≈ arccos(-0.196) ≈ 101.3°
Therefore, the vectors are not orthogonal and the angle between them is approximately 101.3°.
The correct response is: The vectors are not orthogonal. The angle between the two vectors is 101.3°.