For any vectors $\vec { u }$ and $\vec { v }$ , $\| \vec { u } + \vec { v } \| \| \vec { u } - \vec { v } \|$ .

Question

For any vectors $\vec { u }$ and $\vec { v }$ , $\| \vec { u } + \vec { v } \| > \| \vec { u } - \vec { v } \|$ .

Quizplus · Accepted Answer

The inequality does not hold universally because the magnitude of the sum or difference of two vectors depends on their directions relative to each other. For some vectors, the magnitude of their sum may be greater, while for others, the magnitude of their difference may be greater.

For Any Vectors u⃗\vec { u }u And v⃗\vec { v }v

For Any Vectors $\vec { u }$ And $\vec { v }$