Find the dot product, a • b. a = 6i + 5j, b = -5i + 4j?

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: Vectors are a = 6i + 5j and b = -5i + 4j

If vector a = x₁i + y₁j + z₁k and vector b = x₂i + y₂j + z₂k then

Dot product a.b = x₁x₂ + y₁y₂ + z₁z₂

Here, (x₁, y₁, z₁) = (6, 5, 0) and (x₂, y₂, z₂) = (-5, 4, 0)

a.b = (6)(-5) + (5)(4) + (0)(0)

a.b = -30 + 20 + 0

a.b = -10

Therefore, the dot product of given two vectors is -10.

Find the dot product, a • b. a = 6i + 5j, b = -5i + 4j?

Summary:

The dot product a • b, where a = 6i + 5j, b = -5i + 4j, is -10.