Prove that if a = mb +nc where m,neR, then a dot b cross c=0

[wine]

Prove that if a = mb +nc where m,neR, then a dot b cross c=0

I dont really know how i get do it thank you!

 

[Ishuda]

Prove that if a = mb +nc where m,neR, then a dot b cross c=0

I dont really know how i get do it thank you!

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

As a hint, you do know that the [a dot b cross c] must be [a dot (b cross c)] don't you? And that the dot product commutes and distributes.

 

[pka]

Prove that if a = mb +nc where m,neR, then a dot b cross c=0
I dont really know how i get do it thank you!

Do you mean \(\displaystyle (\vec{a}\cdot\vec{b})\times\vec{c}\) or \(\displaystyle \vec{a}\cdot(\vec{b}\times\vec{c})~?\)

 

[wine]

the second one

 

[Ishuda]

the second one

Of course since the dot product is a scalar and the cross product of a scalar and vector is not defined.

As a further hint, since the dot product distributes,
\(\displaystyle \vec{a}\cdot(\vec{b}\times\vec{c})\, =\, m\, [\vec{b}\cdot(\vec{b}\times\vec{c})] + n\, [\vec{c}\cdot(\vec{b}\times\vec{c})]\)

 

[pka]

Of course since the dot product is a scalar and the cross product of a scalar and vector is not defined.

Why of course? I regularly gave the first one on a vector analysis test. To miss it costed twenty points.

 

[Ishuda]

Why of course? I regularly gave the first one on a vector analysis test. To miss it costed twenty points.

Why of course? You are (probably) right at the level of the question being asked but then I wasn't thinking at that level [not to say I never do, just this time I wasn't].