Final answer:
The dot product of the vectors r₁ = 6i + 2j and r₂ = 7i + j is calculated by multiplying their respective components and adding the products together, resulting in a dot product of 44.
Step-by-step explanation:
To calculate the dot product (also known as the scalar product) r₁ ⋅ r₂ of the two vectors r₁ = 6i + 2j and r₂ = 7i + j, you use the formula:
r₁ ⋅ r₂ = (r₁x)(r₂x) + (r₁y)(r₂y)
Where r₁x and r₁y are the components of r₁ and r₂x and r₂y are the components of r₂. Plugging in the values, we get:
r₁ ⋅ r₂ = (6)(7) + (2)(1) = 42 + 2 = 44
So, the dot product of r₁ and r₂ is 44, which corresponds to option B.
To calculate the dot product of two vectors, we multiply their corresponding components and then add them up. Using the given vectors r₁ = 6i + 2j and r₂ = 7i + j, we can calculate the dot product as follows:
r₁ ∙ r₂ = (6)(7) + (2)(1) = 42 + 2 = 44
Therefore, the dot product of r₁ and r₂ is 44.