On occasion, the notation will be a shorthand notation for .
-The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true?

Question

On occasion, the notation  will be a shorthand notation for  .
-The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true? ​  ​

Quizplus · Accepted Answer

Looking at the diagram, we can see that the three vectors are pointing towards the bottom left, bottom right, and top. Since they sum to zero, we can assume that the bottom left and bottom right vectors cancel each other out, leaving only the top vector. Therefore, we can find the angle of the top vector using trigonometry. We know that the sum of the angles in a triangle is 180 degrees, so each angle in an equilateral triangle (which is what we have here) is 60 degrees. The angle between the bottom left and top vectors is also 60 degrees (since they are opposite angles of a parallelogram), so we can use the cosine rule to find the length of the top vector:

cos(60) = (2x^2 - 2x^2cos(60))/2x^2
x = sqrt(3)

Now that we know the length of the vectors, we can see that the coordinates of the top vector are (sqrt(3)/2, 1/2), which matches the coordinates in choice D.

On Occasion, the Notation Will Be a Shorthand Notation