Question

If `vec A xx vec B=vec A xx vec C`, is it correct to conclude that vec B =vec C` ?

Answer 1

Let ` theta _(1)` be the smaller angle between `vec A and vec B, and theta _92)` be the smaller angler between ` vec A` and vec C`
Give ` vec A xxx vec B =vec A xxx vec C`
:. `AB sin theta _(1) hat n_(1) ` are unit vectors in the direction of vectors ` (vec A xxx vec B) and (vec A xx vec C)` respectively..........
Frome (i), ` B sin theta_(1) hatn_(1) = C sin that _(2) hat n_(2) ` ....(ii)
If ` theta_(1) != theta_(2) hat n_(2)`,
If ` thea_(1) != theta_(2) and hat n != hat n _(2),then ` B != C and vec B != vec C`
`If theta_(1) =theta_(2) and hat n_(1) != hat n_(2)`,
then ` B= C and vec B!= vec C` .