The vectors x and y are unit vectors that make and angle of 30 degrees with each other. Calculate the value of | 2x + y | and the direction of 2x + y

Answer: the value of | 2x + y | = 1.39

the direction of 2x + y = 21°

Step-by-step explanation:

Given that the vectors x and y are unit vectors that make and angle of 30 degrees with each other.

Let assume that unit vector x is along the positive x-axis, and unit vector y is at + 30°.

Therefore

2x-y=

2 -

=

and

|2x-y|=√ ((2 - (√2) / 2) ² + (-1/2) ^2)

=1.3862

Therefore the value of | 2x + y | = 1.39

=atan ((-1/2) : (2 - (√2) / 2))

=atan (1.29289/-0.5)

=-0.369 radians

= - 21.143°

Therefore the direction of 2x + y is

21°