Final answer:
To calculate the angle between two vectors, x and y, we can use the dot product formula. The dot product of x and y is -8. The magnitudes of x and y are approximately √11 and √8, respectively. Therefore, the angle between x and y is approximately 127.15 degrees.
Step-by-step explanation:
To calculate the angle between two vectors, x and y, we can use the dot product formula. The dot product of two vectors is equal to the magnitude of the first vector multiplied by the magnitude of the second vector, multiplied by the cosine of the angle between them.
The dot product of x and y is calculated as follows:
x · y = (1)(-2) + (1)(0) + (3)(-2) = -2 - 6 = -8
The magnitudes of x and y are:
|x| = √(1^2 + 1^2 + 3^2) = √(1 + 1 + 9) = √11
|y| = √((-2)^2 + 0^2 + (-2)^2) = √(4 + 0 + 4) = √8
Therefore, the angle between x and y can be found using the formula:
cos(angle) = (x · y) / (|x| * |y|)
cos(angle) = -8 / (√11 * √8)
Using a calculator, the angle between x and y is approximately 127.15 degrees.