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Vectors Angle

Vectors Angle. Reference direction. Vector B. Vector A. Vector A is identical to Vector B , just transported (moved on a graph keeping the same orientation and length). Cartesian CCW = +. Compass CW = +. 1. 4. 2. 3. How to show magnitude of vectors - mathematically and graphically.

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Vectors Angle

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  1. Vectors Angle Reference direction

  2. Vector B Vector A Vector A is identical to Vector B, just transported (moved on a graph keeping the same orientation and length) .

  3. Cartesian CCW = + Compass CW = + 1 4 2 3

  4. How to show magnitude of vectors - mathematically and graphically

  5. Adding two vectors graphically A + B = R Head to tail method

  6. Showing A + B = B + A

  7. Showing A - B ≠ B - A Tail to tail method

  8. Showing A - B = A + (- B)

  9. Breaking vectors down in component parts

  10. V = Vx + Vy + Vz

  11. Adding Vectors mathematically Step 1: Break down vectors to be added into there Vx and Vy components (for three dimension x, y and z components) Step 2: Sum the Vx and then Vy components. Step 3 use the Pythagorean theorem to solve for the magnitude resultant vector Step 4: Use SOH-COA-TOA to find the vector angel from the x axis Example: Add vector A =10 that points to 030º (Cart) with a vector B = 20 that points to 060º (Cart) Step 1: Break vectors into components A = Ax + Ay Ax = Cos 30º (10) = 8.67 Ay = Sin 30º (10) = 5 B = Bx + By Bx = Cos 60º (20) = 10 By = Sin 60º (20) = 17.3 B A

  12. Step 2: Solve for Vx an Vy Vx = Rx = Ax + Bx = 8.67 + 10 = 18.67 Vy = Ry = Ay + By = 5 + 17.3 = 22.3 Step 3: Solve for R (magnitude) |R|2 = Vx2 + Vy2 |R|2 = 18.672 + 22.32 |R|2 = 348.57 + 497.29 = 845.86 |R| = (845.86)1/2 |R| = 29.1 Step 4: Solve for an angle Tan (Vector Angle - from x axis) = 22.3/18.67 = 1.194 Tan -1 (1.194) = 50.1º

  13. Graphical Check 10 10 B B 10 A A

  14. A + B B B A A B A By = 17.3 Ay = 5 Ax = 8.67 Bx = 10 R = A + B = 29.1 Ry = 17.3 + 5 = 22.3 Angle = Tan -1 22.3/18.67 = 50.1º Rx = 8.67 + 10 = 18.67

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