Answer
The distance between x and y is 5$\sqrt {5}$.
Work Step by Step
Note: Vectors can be rewritten using <>, so
x = <10, -3>
y =
To find the distance between two vectors, or dist(x, y), we use the magnitude of the length vector, so
dist(x, y) = ||x - y||
1. Subtract the two vectors:
<10, -3> - = <11, 2>
2. Find the magnitude of the new vector z =<11, 2>: We can find the magnitude using the following formula: $\sqrt {zāz}$ = $\sqrt {a^{2} + b^{2}}$ where . In this problem a = 11 and b = 2. The magnitude can be calculated using the following:
$\sqrt {11^{2} + 2^{2}}$ = $\sqrt {125}$ = 5$\sqrt {5}$
The distance between x and y is 5$\sqrt {5}$.
