PLEASE PLEASE PLEASE HELP! I 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.

Answer 1

Draw the vector on a coordinate plane. Call that point A. Use that as the hypotenuse of a right triangle. Two of your points are B(0,0) and A(2,7). Plot your third point C(2,0) so that it is at the vertex of the right angle of right triangle ABC.

Use the distance formula from Algebra (or the Pythagoren Theorem if that's easier for you) to find the length of the vector - the line that goes from (0,0) to (2,7).

AB = √2² + 7² = √4+49 = √53 ≅ 7.3

Using the law of cosines (c=a²+b²-2abcosγ), find the size of each angle of triangle ABC.

Now for the distance. From (0,0), the vector moves up and to the right. On a map that would be northeast. So, calculate the angle formed by AB and the y-axis (hint: it's the complement of angle B in your triangle). That is your direction. I won't give you the answer, but if it was 20°, it would be written as N 20°E.

Tried to make this sound as simple as possible. Please let me know if you have questions!

Answer 2

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.