Question

What is the value of az . ar?

(a) 1

(b) cos⁡θ

(c) sin⁡θ

(d) 0

The question was asked during an interview for a job.

My question is from Conversion from Cartesian, Cylindrical and Spherical Coordinates in section Vector Differential Calculus of Engineering Mathematics

Answer 1

Correct option is (b) cos⁡θ

For explanation I would say: We first convert ar to Cartesian coordinates. Substituting the values in the formula,

\(\begin{bmatrix}

Px\\

Py\\

Pz\\

\end{bmatrix} \)

\(= \begin{bmatrix}

sin\theta cos⁡φ & cos\theta cos⁡φ & -sinφ\\

sin\theta sin⁡φ & cos⁡\theta sinφ & cosφ\\

cos\theta & -sin\theta & 0\\

\end{bmatrix} \)

\(= \begin{bmatrix}

1\\

0\\

0\\

\end{bmatrix} \), we get cos⁡θ.