Final answer:
To find the angle between two vectors u and v, we can use the dot product formula. The angle between u = 10, 6 and v = -3, 14 is approximately 1.235 radians or 70.75 degrees.
Step-by-step explanation:
To find the angle between two vectors, we can use the dot product formula.
The dot product of two vectors u = 10, 6 and v = -3, 14 can be calculated as:
u · v = 10*(-3) + 6*14 = -30 + 84 = 54
The magnitude of u and v can be calculated using the formula:
|u| = sqrt(10^2 + 6^2) = sqrt(100 + 36) = sqrt(136) ≈ 11.66
|v| = sqrt((-3)^2 + 14^2) = sqrt(9 + 196) = sqrt(205) ≈ 14.32
Using the dot product and magnitudes, we can find the angle between the u and v using the formula:
θ = cos-1(u · v / (|u| * |v|))
θ = cos-1(54 / (11.66 * 14.32))
θ ≈ 1.235 radians or 70.75 degrees