a = (0,4)^{T} is aligned with the Y axis. Its length, 4 units, can be read off the diagram.
Of course, vectors have no fixed location, so vector a could have been drawn anywhere and would have the same length.
The diagram shows the vectors of length 3 and 4, and with a new vector, h.
The length of vector h is harder to figure out. But not much harder, especially if you know about "3, 4, 5 right triangles." The three vectors can be arranged into a right triangle with h as the hypotenuse. The other sides are 3 and 4, so the length of h is 5.
You probably know the Pythagorean Formula:
(length of hypotenuse)^{2} = (length of first side)^{2} + (length of second side)^{2} |
Using this with a right triangle with sides of 3 and 4:
(length of hypotenuse)^{2} = 3^{2} + 4^{2} (length of hypotenuse)^{2} = 9 + 16 = 25 (length of hypotenuse) = 5 |
What is the length of the hypotenuse of a right triangle whose two sides are 6 and 8?