Question

In component form, vector A is 3i + 6j, and vector B is i + 2j. What is the scalar product of these vectors?

Answer 1

Answer:

A.B=(3I+6j).(I+2j)

= 3ii + 6ij + 6 ij + 12 JJ (ii =JJ=kk =1)(ij=jk=Ki=0)

= 3+ 12

=15

Answer 2

Given: We have given two vector, A : 3i + 6j, and B : i + 2j.

To find: The scalar product of these vectors ?

Solution:

• So now we have given two vectors, those are:

                   A = ( 3i + 6j ) and B = ( i + 2j )

• Now we know the formula for scalar or dot product which is:

                   x(vector) = A(vector) . B(vector)

• Now, dot product of i.i is 1 and j.j is 1 and i.j is 0.

                  x = A.B

                   x = ( 3i + 6j ) . ( i + 2j )

                   x = 3i.i + 3i.2j + 6j.i + 6j.2j

                   x = 3(1) + 0 + 0 + 12(1)

                   x = 3 + 12

                   x = 15 = A.B

Answer:

           So the scalar product of the given vectors is 15.