Answer
The distance between u and z is 2$\sqrt {17}$.
Work Step by Step
Note: Vectors can be rewritten using <>, so
u = <0, -5, 2>
z =
To find the distance between two vectors, or dist(u, z), we use the magnitude of the length vector, so
dist(u, z) = ||u - z||
1. Subtract the two vectors:
<0, -5, 2> - = <4, -4, -6>
2. Find the magnitude of the new vector v =<4, -4, -6>: We can find the magnitude using the following formula: $\sqrt {vāv}$ = $\sqrt {a^{2} + b^{2} + c^{2}}$ where . In this problem a = 4 and b = 4 and c = -6. The magnitude can be calculated using the following:
$\sqrt {4^{2} + (-4)^{2} + (-6)^{2}}$ = $\sqrt {68}$ = 2$\sqrt {17}$
The distance between u and z is 2$\sqrt {17}$.
