Answer:
u = (3, 4)T |u| = 5 v = (3, -4)T |v| = 5 w = u + v = (6, 0)T |w| = 6
Of course, 6 < 5 + 5, demonstrating that | u + v | <= | u | + | v |
u = (3, 4)T |u| = 5 v = (3, -4)T |v| = 5 w = u + v = (6, 0)T |w| = 6
Of course, 6 < 5 + 5, demonstrating that | u + v | <= | u | + | v |
That was too easy. Usually vector elements are not convenient integer values. Here are some vectors, represented by column matrices with decimal fractions in their elements:
q = (2.2, 3.6)T r = (-4.8, -2.2)T s = q + r
Of course, the Pythagorean formula still applies, but you will need a calculator to use it.
| (x, y)T | = √( x2 + y2 )
What are the lengths of the vectors?
| q | = | r | = | s | =