Question

vector A × vector B = 0 and vector B × vector C = 0 . prove that vector A ×vector C=0

Answer 1

given that,
vector A × (vector B) = 0
also.
vector C × (vector B) = 0
=> vector A × vector C = 0
{because Euclid's axiom 1}
axiom states that
"things which are equal to each other are equal to one another"
or


alternate method,
vector A × vector B = 0
=> vector A =. 0/ vector B
=>vector A = 0. .......(1) ( because anything divided with zip equals zero )
similarly we have,
vector B = 0 .........(2)

vector A × vector C
= 0 × 0. ( using equation 1 and 2 )
= 0
hence proved