Differentiation of dot product using cartesian components

[CmbkG]

Homework Statement

Show using cartesian components that

d/dt(a.b)=(da/dt).b+a.(da/dt)

The Attempt at a Solution

a= axi+ayj+azk
b=bxi+byj+bzk

a.b=axbx+ayby+azbz

d/dt(a.b)= d/dt(axbx+ayby+azbz)

 

[HallsofIvy]

Homework Statement

Show using cartesian components that

d/dt(a.b)=(da/dt).b+a.(da/dt)

The Attempt at a Solution

a= axi+ayj+azk
b=bxi+byj+bzk

a.b=axbx+ayby+azbz

d/dt(a.b)= d/dt(axbx+ayby+azbz)

Okay, so go ahead and do that! Use the sum rule and product rule.

 

[CmbkG]

Heya, thanks for the reply.

So I've done that nd nw iv got

(da/dt)b+(db/dt)a

do i just put this as the dot product or have i missed out something in my equation?

 

[Pere Callahan]

Heya, thanks for the reply.

So I've done that nd nw iv got

(da/dt)b+(db/dt)a

do i just put this as the dot product or have i missed out something in my equation?

Since you're talking about putting this as a dot product I assume by writing (da/dt)b you meant some different "product" of the two vectors da/dt and b. May I inquire what exactly you were thinking of and how it is related to the dot product (which is where you started from.)

 

[CmbkG]

oh, i see now, i wasn't thinking of them as two vectors but as mulitplying two scalars.

i just forgot what it was i was working with, sorry.

Thanks a lot for your help though, really appreciate it.

 

[Pere Callahan]

i just forgot what it was i was working with, sorry..

It sometimes happens to be useful to pay attention to exactly this particular issue