Find the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places.u=−12i−7j

The magnitude of a vector u = -12i - 7j is calculated using the formula:

||u|| = sqrt((-12)^2 + (-7)^2)

The direction angle (θ) of the vector is calculated using the formula:

θ = atan2(y, x), where x and y are the i and j components of the vector respectively.

Let's calculate:

1. Magnitude: ||u|| = sqrt((-12)^2 + (-7)^2) = sqrt(144 + 49) = sqrt(193) ≈ 13.8924

2. Direction angle: θ = atan2(-7, -12) = -30.2564 degrees

However, because the vector is in the third quadrant, we add 180 degrees to get the actual direction:

θ = -30.2564 + 180 = 149.7436 degrees

So, the magnitude of the vector u is approximately 13.8924 and its direction angle is approximately 149.7436 degrees.