223k views
5 votes
A vector M is given by M=r²aᵣ+sinθaθ. Find the vector in cartesian coordinates.

User LaborEtArs
by
8.7k points

1 Answer

1 vote

Final answer:

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

User Jon Ekiz
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories