Question

If v lies in the first quadrant and makes an angle π/3 with the positive x-axis and |v| = 4, find v in component form.

Answer 1

v = <2, 2√3>

Explanation:

Let v be the vector of form <x,y>

Since its determinant is |4|, then:

`x^2 +y^2 =4^2=16`

If it makes a π/3 angle with the positive x-axis, then the tangent relationship yields:

`tan(\pi/3) = 1.732=(y)/(x)\\3x^2=y^2`

Replacing in the first equation:

`x^2 +3x^2 =16\\x=2\\y=√(16-4)\\ y=2\sqrt 3`

Therefore, v can be represented in component form as v = <2, 2√3>.