Addition of Vectors?

Question

There is a vector pointing due north w/ a magnitude of 6, a vector pointing 30 degrees from the positive x-axis w/ a magnitude of 5, and a vector pointing due east w/ a magnitude of 7. I'm supposed to add the vectors together and find the sum of the resultant vector and it's magnitude....any help?

Answer 1

Greetings,

find the components of the vector at 30 degress

The horizontal component along the x-axis is 5cos30 = 5sqrt3/2

the vertical component along the y-axis is 5sin30 = 2.5

Now add the vertical and horizontal components

6 + 2.5 = 8.5 units north

7 + 5sqrt3/2 units east

resultant vector has length sqrt(8.5^2 + (7 + 5sqrt3/2)^2) = 14.164

The angle from the positive x-axis is tan^-1(8.5/11.33) = 36.88 degrees

Regards