Worksheet for Vector Dot / Scalar product Calculation
Vector dot product is used to describe the product of physical quantities which have both a magnitude and a direction associated with them. The Dot Product also known as Scalar Product. The dot product of two vectors in the same direction is equal to the product of their magnitudes. The scalar product of two perpendicular vectors is zero. This worksheet help you to understand how to perform vector dot product.
Vector dot/scalar product properties: The Scalar or Dot product of the vectors properties are
1. The commutative Law A . B = B . A
2. The Distributive Law A . (B + C) = A. B + A . C
3. A (B . C) = B . (AC)
4. A . A >= 0; and A. A = 0 if and only if A = o
Example problem: Let the two vectors be A, B and C is the resultant vector. The inputs are in the ijk format.
C = A . B
A = 1i+2j+3k
B = 4i+5j+6k
Then the resultant vector C = A . B
C =(1x4) + (2x5) + (3x6)
The resultant vector dot product is 32