Final answer:
To find the angle between two vectors a and b, you can use the dot product formula. In this case, the angle between the vectors (a) a s = -2.00nd 6.00ne and b s = 2.00nd − 3.00ne is approximately 127.94°.
Step-by-step explanation:
For (a), we can find the angle between two vectors by using the dot product formula:
a . b = |a| |b| cos θ
First, we find the dot product of the two vectors:
a . b = (-2)(2) + (6)(-3) = -4 - 18 = -22
Then, we find the magnitudes of the vectors:
|a| = √((-2)^2 + 6^2) = √4 + 36 = √40 = 2√10
|b| = √(2^2 + (-3)^2) = √4 + 9 = √13
Finally, we can plug the values into the formula to find the angle:
-22 = (2√10)(√13) cos θ
cos θ = -22 / (2√10)(√13) ≈ -0.564189
θ ≈ arccos(-0.564189) ≈ 127.94°
Therefore, the angle between vectors a and b is approximately 127.94°.