Answer:
v = <2, 2√3>
Step-by-step explanation:
Let v be the vector of form <x,y>
Since its determinant is |4|, then:
[tex]x^2 +y^2 =4^2=16[/tex]
If it makes a π/3 angle with the positive x-axis, then the tangent relationship yields:
[tex]tan(\pi/3) = 1.732=\frac{y}{x}\\3x^2=y^2[/tex]
Replacing in the first equation:
[tex]x^2 +3x^2 =16\\x=2\\y=\sqrt{16-4}\\ y=2\sqrt 3[/tex]
Therefore, v can be represented in component form as v = <2, 2√3>.
