SOLUTION: The vector x and y are unit vectors (vectors with the magnitude 1) that make an angle of 30 degrees with each other. a)calculate the value of |2x-y| b)determine the direction of

Question 1084399: The vector x and y are unit vectors (vectors with the magnitude 1) that make an angle of 30 degrees with each other.
a)calculate the value of |2x-y|
b)determine the direction of 2x-y
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
The vector x and y are unit vectors (vectors with the magnitude 1) that make an angle of 30 degrees with each other.
a)calculate the value of |2x-y|
b)determine the direction of 2x-y

Solution:
Without loss of generality, we will assume unit vector x is along the positive x-axis, and unit vector y is at +30°.
Therefore
2x-y=
2< 1,0 > - < cos(30),sin(30) >
=<2-(√2)/2, 0-1/2>
and
|2x-y|=√((2-(√2)/2)² + (-1/2)^2)
=1.3862
Angle
=atan((-1/2)÷(2-(√2)/2))
=atan(1.29289/-0.5)
=-0.369 radians
= -21.143°

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