How to Prove Vector Property for R(t) = <f(t), g(t), h(t)>

[multivariable]

I can't seem to figure out how to prove the property for R(t) = <f(t), g(t), h(t)> :

Dt[R(t) X R'(t)] = R(t) X R"(t)

Any suggestions?!

 

[lurflurf]

is X cross product?
[R(t) X R'(t)]' = R'(t) X R'(t)+R(t) X R"(t)
for any sensible derivative
thus
[R(t) X R'(t)]' = R(t) X R"(t)
if and only if
R'(t) X R'(t)=0
clearly true for cross product

 

[HallsofIvy]

I can't seem to figure out how to prove the property for R(t) = <f(t), g(t), h(t)> :

Dt[R(t) X R'(t)] = R(t) X R"(t)

Any suggestions?!

Homework Statement

Homework Equations

The Attempt at a Solution

Is the "Dt" derivative with respect to t? i.e.(R x R')' ?

What have you tried? Have you tried actually writing out each side in terms of derivatives of f, g, and h?

Do you know that the "product rule" from Calculus I is still true for vector products? What does that give you?

 

[multivariable]

wow.. I had copied the property [R(t) x R'(t)]' = blah blah blah.. incorrectly from my book... It makes perfect sense now, thank you for the help!