Chapter 12 - Vectors (3D)

Question 1

How do you calculate the distance from the origin to the point (x, y, z)?

Answer 1

sq root (x² + y² + z²)

Question 2

How do you calculate the distance between (x₁, y₁, z₁) and (x₂, y₂, z₂)?

Answer 2

sqroot [(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Question 3

If the vector a = xi + yj + zk makes an angle θ_x with the positive x axis, how do you calculate cos θ_x?

Answer 3

= x / | a |

Similarly cos θ_y = y / | a |

and cos θ_z = z / | a |