PLEASE PLEASE HELP ME! NEED HELP WITH GEOMETRY HOMEWORK!

Question

Find the magnitude and direction of the vector < 2,7>. Round angles to the nearest degree and other values to the nearest tenth. Please Give me the Explanation and the Answer.

Answer 1

Use the formulas for magnitude and direction.

Magnitude of <x,y> = √(x² + y²)

Direction θ of <x,y> satisfies θ = arctan(y/x). You need to determine the appropriate quadrant.

For example, the magnitude of <1,3> is √(1 + 9) = √10 ~ 3.2 and the direction is θ = arctan(3/1) ~ 71.6 degrees.

Answer 2

Vector <2,7> can be drawn starting at (0,0) to point, (2,7). The magnitude is the Pythagorean Theorem

V = SquareRoot (x² + y²) = √(2² + 7²) = √(4 + 49) = √(53) = 7.28

at an angle of Tan^-1 (7/2) = 74.05 °