Question

A vector M is given by M=r²aᵣ+sinθaθ. Find the vector in cartesian coordinates.

Answer 1

To find the vector in cartesian coordinates, you need to convert the polar coordinates (r, θ) into Cartesian coordinates (x, y). The vector M in Cartesian coordinates is (x² + y²)aᵣ + yaθ.

Step-by-step explanation:

Solution:

To express the given vector M = r²aᵣ + sinθaθ in Cartesian coordinates, we need to convert the polar coordinates (r, θ) into Cartesian coordinates (x, y).

Using the equations x = rcosθ and y = rsinθ, we can rewrite the vector M in Cartesian coordinates as:

M = (r²cosθ)aᵣ + (rsinθ)aθ

Since r² = x² + y² and cosθ = x/r, sinθ = y/r, the vector M in Cartesian coordinates is:

M = (x² + y²)aᵣ + yaθ