Find the direction of the following vector: $u⃗=\langle\frac{5\surd3}{3},5\rangle$.

• A. 60°
• B. 0.030°
• C. 30°
• D. 0.010°

Answer: (A)

Verified step by step guidance

1. First, understand that the direction of a vector is given by the angle it makes with the positive x-axis. This angle can be found using the tangent function, which relates the components of the vector.
2. The vector u⃗ is given as ⟨\frac{5\sqrt{3}}{3}, 5⟩. Here, \frac{5\sqrt{3}}{3} is the x-component and 5 is the y-component.
3. To find the angle θ, use the formula \tan(θ) = \frac{y}{x}, where y is the y-component and x is the x-component of the vector.
4. Substitute the values into the formula: \tan(θ) = \frac{5}{\frac{5\sqrt{3}}{3}}.
5. Solve for θ by taking the arctangent of the result from the previous step: θ = \arctan\left(\frac{5}{\frac{5\sqrt{3}}{3}}\right). This will give you the direction of the vector in degrees.