Question

What is `||<< -6,-7,1 >>||` (the magnitude of `<< -6, -7, 1 >>`)?

Answer 1

Well, the magnitude of an `N`-dimensional vector is determined via an "expanded" form of the Pythagorean Theorem:

`\mathbf(||<< n_1, n_2, ..., n_N >>|| = sqrt(n_1^2 + n_2^2 + ... + n_N^2))`

where `n` is a specific dimension (like `x`, `y`, or `z`), and `N` is the number of dimensions.

To get the magnitude of this vector:

`||<< -6,-7,1 >>||`

`= sqrt((-6)^2 + (-7)^2 + 1^2) = sqrt(86)`

`~~ color(blue)(9.2736)`