Calculus Question: The vectors x and y are unit vectors...

Question

The vectors x and y are unit vectors (vectors with magnitude 1) that make an angle of 30^o with each other. Please show all work, thank you!

a) Calculate the value of |2x - y|

b) Determine the direction of 2x - y

Answer 1

a) I2x - yI² = (2x - y)² = 4IxI² - 4x•y + IyI² = 4 - 4cos30° + 1 = 5 - 2√3; so I2x - yI = (5 - 2√3)^1/2

b) Let angle between (2x - y) and x is θ.

Then cosθ = (2x - y)•x/[I2x - yI·IxI] = (2 - cos30)/(5 - 2√3)^1/2= (4 - √3)/[2(5 -2√3)^1/2] = .915

θ = cos^-10.915 = 23.8°

Yes, x means vector x and IxI means magnitude of vector x which is 1 for x.