Question

multiple choice question
the relationship between direction cosines cos θₓ, cos θᵧ, and cos θₙ is given by:
o cos²θₓ + cos²θᵧ + cos²θₙ = 1.
o cos θₓ + cos θᵧ + cos θₙ = 1.
o cos θₓ - cos θᵧ - cos θₙ = 0.
o cos²θₓ - cos²θᵧ - cos²θₙ = 0.

Explanation:

Step1: Recall direction - cosine property

In three - dimensional space, for a vector, the sum of the squares of its direction cosines is always 1.

Step2: Identify the correct formula

The formula for the relationship between direction cosines $\cos\theta_x$, $\cos\theta_y$, and $\cos\theta_z$ is $\cos^{2}\theta_x+\cos^{2}\theta_y+\cos^{2}\theta_z = 1$.

Answer:

$\cos^{2}\theta_x+\cos^{2}\theta_y+\cos^{2}\theta_z = 1$ (corresponding to the first option in the multiple - choice question)