USA: +1-585-535-1023

UK: +44-208-133-5697

AUS: +61-280-07-5697

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.

Work  =w =f .d = fd cos θ.

Note that work is a scalar quantity


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