Find a.b if a = 4i - 4j, b = 4i + 5j

Solution:

Dot Product of vectors is equal to the product of the magnitudes of the two vectors, and the cosine of the angle between the two vectors.

The resultant of the dot product of two vectors lie in the same plane of the two vectors.

The dot product may be a positive real number or a negative real number.

Given,

\(\vec{a}\) = 4i - 4j and  \(\vec{b}\) = 4i + 5j

If \(\vec{a}\)= x₁i + y₁j +z₁k and\(\vec{b}\) = x₂i + y₂j +z₂k, then

\(\vec{a}\times \vec{b}\) = x₁x₂ + y₁y₂ +z₁z₂

Here, (x₁, y₁) = (4, -4) and (x₂, y₂) = (4, 5)

\(\vec{a}\times \vec{b}\) = (4 × 4) + (-4 × 5) = -4

Find a.b if a = 4i - 4j, b = 4i + 5j

Summary:

If a = 4i - 4j, b = 4i + 5j, a.b = -4.