   Chapter 12.3, Problem 64E

Chapter
Section
Textbook Problem

# Show that if u + v and u − v are orthogonal, then the vectors u and v must have the same length.

To determine

To show: the vectors u and v has same length, when u+v and uv are orthogonal.

Explanation

Given:

Two vectors u and v.

Formula used:

Condition for orthogonal:

Two vectors u and v are orthogonal if and only if uv=0 .

Find the dot product between (u+v)(uv) .

(u+v)(uv)=uuuv+vuvv=uuuv+vuvv=|u|2uv+vu|v|2 (vv=|v|2uu=|u|2)=|u|2u<

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