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Scalar or Dot Product of Two Vectors

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

Again

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