Find the direction angle of each vector. v= -7i-4j

Answer 1

The "i-direction" lines up with what we typically call the x-direction and "j" lines up with "y". So -7i - 4j ends at the point (-7, -4).

The angle θ can be found using the trig ratio tangent: tan(θ) = opp/adj = 4/7 so θ = 29.74° however, we typically measure the angle from the positive "x" axis so we need to add 180° to that number so the direction angle of the vector is 180+29.74 = 209.74°

Note: There are other ways of referencing the angle, for instance if measured as a bearing, we start at North which we call the positive "y" axis. So you'll need to double check that the statement I made "we typically measure the angle from the positive "x" axis" is true based on your teacher's instructions or your book.

Answer 2

draw and label a diagram!

tan θ = 4 / 7, In QIII