Question

find the angle between the vectors. (first find an exact expression and then approximate to the nearest degree.) 15. u − k 5, 1 l, v − k 3, 2 l

Answer 1

The angle between the vectors u = 15u - k and v = 5i + lj - 3k is approximately 29.64 degrees.

Step-by-step explanation:

To find the angle between the vectors u = 15u - k and v = 5i + lj - 3k, we can use the dot product formula:

cos(theta) = (u · v) / (|u| * |v|)

First, let's calculate the dot product:

u · v = (15 * 5) + (1 * 0) + (-1 * -3) = 78

Then, let's calculate the magnitudes of the vectors:

|u| = sqrt((15 * 15) + (1 * 1) + (-1 * -1)) ≈ 15.36

|v| = sqrt((5 * 5) + (1 * 1) + (-3 * -3)) ≈ 5.83

Now, we can substitute these values into the formula:

cos(theta) = 78 / (15.36 * 5.83) ≈ 0.8812

Finally, we can find the angle theta by taking the inverse cosine:

theta ≈ acos(0.8812) ≈ 29.64 degrees