Vectors Angle Reference direction. Vector A is identical to Vector B, just transported (moved on a...
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Transcript of Vectors Angle Reference direction. Vector A is identical to Vector B, just transported (moved on a...
Vectors Angle
Reference direction
Vector A is identical to Vector B, just transported (moved on a graph keeping the same orientation and length) .
Vector A
Vector B
Cartesian CCW = +
Compass CW = +1
23
4
How to show magnitude of vectors - mathematically and graphically
Adding two vectors graphically
A + B = R
Head to tail methodHead to tail method
Showing A + B = B + A
Showing A - B ≠ B - A
Tail to tail methodTail to tail method
Showing A - B = A + (- B)
Breaking vectors down in component parts
V = Vx + Vy + Vz
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)
A
B
Step 1: Break vectors into components
A = Ax + Ay
Ax = Cos 30º (10) = 8.67
Ay = Sin 30º (10) = 5
B = Bx + ByBx = Cos 60º (20) = 10By = Sin 60º (20) = 17.3
Adding Vectors mathematically
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
A
B
Graphical CheckGraphical Check
B
A
10
10
10
A
B
A
A + BB
AAy = 5
Ax = 8.67
By = 17.3
Bx = 10
B
Ry = 17.3 + 5 = 22.3
Rx = 8.67 + 10 = 18.67
R = A + B = 29.1
Angle = Tan -1 22.3/18.67 = 50.1º