Vector magnitude

The magnitude of the vector is equal to the length of the vector itself,. But how do we calculate it mathematically? .

The magnitude of a vector is given by the Pythagorean theorem, which specifies that in a right triangle , the square of length of a diagonal is equal to the sum of the squares of the adjacent sides. So when we look at the right triangle as follows, c2 = x2 + y2.

This can be extended to three dimensions with c2 = x2 + y2 + z2.

Magnitudes of vectors are indicated by double vertical bars, so the magnitude of a
vector  is denoted by . The magnitude is always greater than or equal to zero.

So, if vector A = (X, Y, Z) then the magnitude is given by the following equation: 

If  = (3, -5, 7), Then:

 

= 9.110

The vector   is therefore 9.11 units long