q = (2.2, 3.6)T r = (-4.8, -2.2)T s = q + r
| |q| | = | √( 2.2*2.2 + 3.6*3.6 ) | = | √( 4.84 + 12.96 ) | = | √17.8 | = | 4.219 |
| |r| | = | √( -4.8* -4.8 + -2.2 * -2.2 ) | = | √( 23.04 + 4.84 ) | = | √27.88 | = | 5.280 |
| |s| | = | √( -2.6 * -2.6 + 1.4*1.4 ) | = | √( 6.76 + 1.96 ) | = | √8.72 | = | 2.953 |
As expected, |s| is less than |q| + |r|.
Three dimensional vectors have length. The formula is about the same as for two dimensional vectors. The length of a vector represented by a three-component matrix is:
|
|(x, y, z)T| = √( x2 + y2 + z2) |
For example:
|(1, 2, 3)T| = √(12 + 22 + 32) = √( 1 + 4 + 9 ) = √14 = 3.742
What is the length of (2, -4, 4)T
What is the length of (-1, -2, 3)T