Question

For vectors to be parallel the whole vector needs to be the scalar multiple or only the individual components need to be the scalar multiple?

Answer 1

For example is <3,2,1> parallel to <6,4,3> individual components are multiples but not the whole vector is a scalar multiple?

Answer 2

\[\langle6,4,3
\rangle=2\langle3,2,\tfrac32\rangle\neq\alpha\langle3,2,1\rangle\]

Answer 3

That means the whole needs to be the scalar multiple of a single number. Thanks!

Answer 4

right. the vectors are only scalar multiples when all of the corresponding components are in the same ratios