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(Solved): Problem 3. Show that if for all t we have ||vec(v)(t)||^(2)=vec(v)(t)*vec(v)(t)=c for some nonnegati ...
Problem 3. Show that if for all t we have ||vec(v)(t)||^(2)=vec(v)(t)*vec(v)(t)=c for some nonnegative
scalar cinR, then
vec(v)(t)*vec(v)^(')(t)=0
Note that this means the position vector vec(v)(t) is orthogonal to direction vecto(r)/(v)elocity vec(v)^(')(t)
if the vector vec(v)(t) has constant lengt(h)/(m)agnitude.
Hint. Use the dot-product property of differentiating a vector-valued function from Section
3.2, p. 245.