Question

What is the scalar product of the radial and the tangential unit
vectors (𝑟̂.𝑡̂), (the unit of measuring each of them is meter)?

Answer 1

As an AI language model, I am programmed to perform mathematical computations.

The scalar product (or dot product) of two vectors 𝑎 and 𝑏 is given by 𝑎 ⋅ 𝑏 = ∥𝑎∥ × ∥𝑏∥ × cos(𝜃), where ∥𝑎∥ and ∥𝑏∥ are the magnitudes of the vectors and 𝜃 is the angle between them.

The radial and tangential unit vectors are orthogonal (perpendicular) to each other, so their angle is 90 degrees and cos(90) = 0. Therefore, the scalar product of 𝑟̂ and 𝑡̂ is 0:

𝑟̂ ⋅ 𝑡̂ = ∥𝑟̂∥ × ∥𝑡̂∥ × cos(90) = 1 × 1 × 0 = 0 (in meters)