Final answer:
To find the angle between vectors a and b, we can use the dot product formula and the magnitude of the vectors. The dot product of two vectors a and b is given by the expression a · b = |a| * |b| * cos(theta), where theta is the angle between the vectors.
Step-by-step explanation:
To find the angle between the vectors a and b, we can use the dot product formula and the magnitude of the vectors. The dot product of two vectors a and b is given by the expression a · b = |a| * |b| * cos(theta), where theta is the angle between the vectors. Rearranging the formula, we have cos(theta) = (a · b) / (|a| * |b|). From the given vectors, a = <4, 2> and b = <-2, -2>. The dot product of a and b is (4 * -2) + (2 * -2) = -14. The magnitude of vector a is |a| = sqrt((4^2) + (2^2)) = sqrt(20) = 2sqrt(5), and the magnitude of vector b is |b| = sqrt((-2)^2 + (-2)^2) = sqrt(8) = 2sqrt(2).
Substituting these values into the formula, we have cos(theta) = (-14) / (2sqrt(5) * 2sqrt(2)). Simplifying, we get cos(theta) = -14 / (4sqrt(10)) = -7 / (2sqrt(10)). To find the angle theta, we can take the inverse cosine of cos(theta). Finally, we can convert the angle from radians to degrees by multiplying by 180 and dividing by pi.