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How to Calculate a VDP

VDP stands for a vector dot product. A vector is an object in geometry that has both length and direction. A vector is defined by Cartesian coordinates (X,Y) of initial (X1,Y1) and terminal points (X2,Y2) and is represented by a line with an arrow. The dot product of two vectors is a number (scalar) and is widely used in physics. As an example, calculate VDP if vectors defined by the points with Cartesian coordinates (2,-3), (4,6) and (2,-3), (7,5) and the angle between the vectors is 24 degrees.

Calculator

Instructions

- 1
  Calculate the length of the first vector using the formula:
  sqrt((X2 - X1)^2 + (Y2 - Y1)^2)
  "Sqrt" is an abbreviation for the root square math operation.
  In our example, the first vector length is:
  sqrt((4-2)^2 + (6 - (-3))^2) = sqrt(4 + 81 ) = 9.22
- 2
  Calculate the length of the second vector using the same formula as in Step 1. In our example, the second vector length is:
  sqrt((7 - 2)^2 + (5 - (-3))^2) = sqrt(25 + 64 ) = 9.43
- 3
  Calculate cosine of the angle using the function "cos" on your calculator. In the example, cos(24) is 0.9135.
- 4
  Multiply the first vector length, the second vector length and the cosine of the angle to calculate VDP. In our example, VDP equals:
  9.22 * 9.43 * 0.9135 = 79.42

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