# show inequality of distance between vectors

• February 12th 2011, 07:07 PM
Jskid
show inequality of distance between vectors
Define the distance between two vectors u and v in $R^n$ as d(u, v) = ||u-v||Show that d(u, w) <= d(u, v) + d(v, w)

My work:
$||u-v|| + ||v+w||=\sqrt{(u_1-v_1)^2+(u_2-v_2)^2+...+(u_n-v_n)^2}+\sqrt{(v_1-w_1)^2+(v_2-w_2)^2+...+(u_n-w_n)^2}$
• February 15th 2011, 05:10 AM
HallsofIvy
Can you use the fact that $||u+ v||\le ||u||+ ||v||$?