Given the vector → u = ⟨ 4 , − 4 ⟩

Question

find the magnitude and angle in which the vector points (measured counterclockwise from the positive x-axis, )

Answer 1

Hello Danny,

The vector is given to you in the form u = ⟨ x , y ⟩ where x = 4 and y = -4

First, you'd want to draw it on a coordinate grid. Starting from the origin, you go RIGHT 4 (because x = 4) then DOWN 4 (because y = -4). That will place vector u in quadrant 4. Keep that in mind.

The formula for magnitude: magnitude = square_root(x^2 + y^2)

----> magnitude = √(4^2 + (-4)^2) = √(16+16) = √32 = 4√2

angle = tan^-1(y/x)

---> angle = tan^-1(-4/4) = tan^-1(-1) = (Leaving this last step for you to solve)

Remember that the vector is in quadrant 4. If you look at a unit circle, which angle in quadrant 4 has a tangent equal to -1? Once you find it, that will be your answer.

Recap: magnitude = 4√2

angle = the angle you'll find in Quadrant 4 that has a tangent equal to -1.

Cheers.