SCALAR OR DOT PRODUCT OF TWO VECTORS
Let A and B vectors make 8 as included angles as shown in Fig. 2.8. The scalar or Dot product is defined as A . B = | A | | B | cos θ, where θ is smaller angle between the two vectors. The ‘work’ is the result of the scalar product of vectors force with displacement.
Thus, dot product is commutative.
We know that projection of the sum of two vectors is the same as the sum of the projections of the vectors.
i. j=0 I .i=1
I .k=0 here θ =900 j .j =2 here θ =o0
k .j =0 K.K =1
If we write the vectors A and B in cartesian components and do the dot product, we get
=Ax B x +Ay By +A z B z
It means that a scalar product of two vectors is the sum of the ordinary products of the respective components