Final answer:
To find the angle between the vectors u = 9i+6j and v = -2i+j, we can use the dot product formula. The angle is approximately 121.26°.
Step-by-step explanation:
To find the angle between the vectors u = 9i+6j and v = -2i+j, we can use the dot product formula:
u · v = |u| |v| cos θ
where |u| and |v| are the magnitudes of the vectors, and θ is the angle between them.
First, let's calculate the magnitudes:
|u| = √(9² + 6²) = √117 = 10.82
|v| = √((-2)² + 1²) = √5 = 2.24
Now, let's calculate the dot product:
u · v = (9)(-2) + (6)(1) = -18 + 6 = -12
Finally, we can find the angle:
-12 = (10.82)(2.24) cos θ
cos θ = -12/(10.82)(2.24) ≈ -0.5274
θ ≈ cos⁻¹(-0.5274) ≈ 121.26°