Linear Algebra - Distance In 3 Dimensions

Question

show in full detail why the distance from the original to the tip of vector a=[5,−3,4] is given by sqrt of 5²+(−3⁾²+4². You may use the 2D version of the Pythagorean Theorem.

Answer 1

I think you meant to say "the distance from the ORIGIN to the tip..."

The distance from the origin to the tip is just the magnitude of the vector, which is given by

|a| = √(a•a) = √(a_x² + a_y² + a_z²)

You know a_x, a_y, and a_z. Plug them into the equation.