Find the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places.u=−7i−6j

The magnitude of a vector u = -7i - 6j is calculated using the formula:

||u|| = sqrt((-7)^2 + (-6)^2)

First, square each component:

(-7)^2 = 49 (-6)^2 = 36

Then, add these values together:

49 + 36 = 85

Finally, take the square root of this sum:

sqrt(85) ≈ 9.2195

So, the magnitude of the vector u is approximately 9.2195.

The direction angle θ of a vector u = -7i - 6j is calculated using the formula:

θ = atan2(-6, -7)

This function atan2(y, x) returns the angle in radians between the positive x-axis and the point given by the coordinates (x, y).

atan2(-6, -7) ≈ -2.4981 radians

To convert this to degrees, multiply by 180/π:

-2.4981 * (180/π) ≈ -143.1301 degrees

However, since we usually express the direction angle as a positive value between 0 and 360 degrees, we add 360 to this result:

-143.1301 + 360 = 216.8699 degrees

So, the direction angle of the vector u is approximately 216.8699 degrees.