(Graph with line from (-5,0) to (7,2))

Find the direction angle of vector v to the nearest tenth of a degree.

Equation editor does not include the grouping symbols "<" and ">" that are necessary for writing a vector in component form. For this question, use braces to write a vector in component form. For example, the vector <2,3> should be written as {2,3}.

direction vector = <7+5, 2-0> = <12,2>

direction angle = tan^-1 (2/12) = appr 9.5° or appr 0.165 radians

To find the direction angle of a vector, we can use the formula:

Θ = tan^(-1)(v_y / v_x)

where v_x is the x-component of the vector and v_y is the y-component of the vector.

Given the two points (-5,0) and (7,2), we can find the components of the vector v by subtracting the corresponding coordinates. Let's calculate the components:

v_x = 7 - (-5) = 12
v_y = 2 - 0 = 2

Now, substitute these values into the formula:

Θ = tan^(-1)(2 / 12)

To evaluate this using a calculator, follow these steps:

1. Make sure your calculator is in degree mode.
2. Enter the fraction 2 / 12.
3. Press the inverse tangent button (often written as "tan^(-1)" or "arctan") on your calculator.

After performing these steps, you should get the direction angle Θ. Round this value to the nearest tenth of a degree as requested.