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. 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
What is the length of