Find a.b if a = 7i - 4j, b = 4i + 3j

Solution:

Given, a = 7i - 4j, b = 4i + 3j

We have to find a.b

If the two vectors are expressed in terms of unit vectors, i, j, k, along the x, y, z axes, then the scalar product is given by

a.b = a₁b₁ + a₂b₂ + a₃b₃

Here, a₁ = 7, a₂ = -4, b₁ = 4 and b₂ = 3

a.b = (7i - 4j).(4i + 3j)

= 7(4) + (-4)(3)

= 28 - 12

= 16

Therefore, a.b = 16

Find a.b if a = 7i - 4j, b = 4i + 3j

Summary:

If a = 7i - 4j, b = 4i + 3j, then a.b is 16.