Find the length of the arrow joining the point \(P(4,-1,11)\) to the point \(Q(-2,6,4)\) in \(\RNrSpc{3}\).
The length of the arrow \(\Arrow{P}{Q}\) is the distance from \(P\) to \(Q\):
| \(\Length{\Arrow{P}{Q}}\) | \(=\) | \(\Dstnc{P}{Q}\) |
| \(\) | \(=\) | \(\sqrt{(-2-4)^2+(6-(-1))^2+(4-11)^2}\) |
| \(\) | \(=\) | \(\sqrt{36+49+49}\) |
| \(\) | \(=\) | \(\sqrt{134}\) |
Find the length of the arrow joining the point \(A(1,3,0,5)\) to the point \(B(2,1,-2,4)\) in \(\RNrSpc{4}\).
The length of the arrow \(\Arrow{A}{B}\) is the distance from \(A\) to \(B\):
| \(\Length{\Arrow{A}{B}}\) | \(=\) | \(\Dstnc{A}{B}\) |
| \(\) | \(=\) | \(\sqrt{(2-1)^2 + (1-3)^2 + ((-2)-0)^2 + (4-5)^2 }\) |
| \(\) | \(=\) | \(\sqrt{1 + 4 + 4 + 1}\) |
| \(\) | \(=\) | \(\sqrt{10}\) |