vectors

ABCDEF is a regular hexagon with sides of unit length. Find the magnitude and the direction of AB+AC+AD+AE+AF.

The textbook answer: 6, 60 degrees to AB

A full solution with steps will be greatly appreciated.
Thank you :)

  1. 👍
  2. 👎
  3. 👁
  1. https://answers.yahoo.com/question/index?qid=20090914114948AAF9qjv

    1. 👍
    2. 👎
    👤
    bobpursley
  2. I put A at lower left and B a lower right.
    AB = 1 i + 0 j
    AC = (1+cos 60)i + sin 60 j
    AD = 1 i + 2 sin 60 j
    AE = 0 i + 2 sin 60 j
    AF = -cos 60 i + sin 60 j
    sum of x components = 3
    sum of y components = 6 sin 60 = 6 (sqrt3 /2) = 3 sqrt 3
    magnitude = sqrt(3^2 + 9*3) = sqrt 36 = 6 sure enough
    tan angle = sqrt 3 /1
    so angle = 60

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    1. Which polygon will always be irregular? A. triangle B. trapezoid** C. square D. hexagon 2. Which statements are always true about regular polygons? (Choose 2) A. All sides are congruent B. Pairs of sides are parallel** C. All

  2. Math please helppp

    1 Find the missing angle measure in the polygon A ] 77 B ] 87 C ] 97 D ] 107 i think its b 2 Find the sum of the interior angles in 10 - sided polygon A ] 1,260 B ] 1,440 c ] 1,620 d ] 1,800 i think its c or b 3 Find the measure

  3. help hexagon geometry

    A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio of the area of the larger hexagon to the area of the smaller hexagon? Express your answer as a common

  4. Maths

    If ABCDEF is a regular hexagon then prove that ab+ac+ad+ea+fa=4ab

  1. math

    Sides $\overline{AB}$ and $\overline{EF}$ of regular hexagon $ABCDEF$ are extended to meet at point $P$. What is the degree measure of angle $P$?

  2. easy geometry

    1)If diagonals of a rhombus are 10 cm and 24 cm. find the area and perimeter of the rhombus. 2)A regular hexagon with a perimeter of 24 units is inscribed in a circle. Find the radius of the circle. 3)Find the altitude,perimeter

  3. geometry

    1. An exterior angle of a regular polygon measures 30 degrees. What is the measure of an interior angle? 30 60 120 150 2. How many degrees are in each interior angle of a regular pentagon? 50 72 108 120 3. If all of the diagonals

  4. Geometry

    Hi, I'm having a difficult time understanding a couple of Geometry questions on my homework and I'd really appreciate it if someone could answer them and explain to me how to get the same answer. Question 1: A regular pentagon has

  1. geometry

    find the area of a regular hexagon with the side length 4m. round to the nearest tenth

  2. math

    Two regular hexagons are similar. The perimeters have a ratio of 5: 2. If the side of the larger hexagon has a length of 25 inches, what is the perimeter of the smaller hexagon? AND COULD SOMEONE PLEASE ANSWER IT!?

  3. Geometry / Trig

    What is the area of a regular hexagon with a distance from its center to a vertex of 1 cm? (Hint: A regular hexagon can be divided into six equilateral triangles.) hex The area of the regular hexagon is _____ ?

  4. physics

    Four masses are positioned at the corners of a rectangle, as indicated in the figure below (not to scale). (a) Find the magnitude and direction of the net force acting on the 2.0 kg mass if x = 0.40 m and y = 0.12 m. (b) How do

You can view more similar questions or ask a new question.