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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.

User Deitsch
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1 Answer

4 votes

Answer:

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>.

User BlackWasp
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