Λa+µb+vc =0 constants not all zero c.(axb)=0

[indie452]

Homework Statement

past paper qu...

λa + µb + vc = 0
for some λ, µ, v not all zero show c.(axb)=0

consider cases v not equal to 0 and v = 0

The Attempt at a Solution

not sure how to start so if someone could just point me in the right direction or offer another hint it may help me get started in the mean time i'll keep looking at it

thanksok i think i made a bit of progress:-

when v not= 0
λa.(axb) + µb.(axb) + vc.(axb) = 0.(axb)

so vc.(axb) = 0
=> c.(axb) = 0

 

[Dick]

Use properties of the dot and cross product. axb is perpendicular to both a and b, right?
So a.(axb)=b.(axb)=0. And if a and b are parallel, then axb=0.

 

[indie452]

Use properties of the dot and cross product. axb is perpendicular to both a and b, right?
So a.(axb)=b.(axb)=0. And if a and b are parallel, then axb=0.

ok this along with the progress i made earlier has helped me do the qu

thanks a lot