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} | = √( x^{2} + y^{2} + z^{2}) |

For example:

| (1, 2, 3)^{T}| = √( 1^{2}+ 2^{2}+ 3^{2}) = √( 1 + 4 + 9 ) = √14 = 3.742

What is the length of (2, -4, 4)^{T}

What is the length of (-1, -2, 3)^{T}