Question

Vectors a=[-3,2] and vector b=[6,t-2]. Determine t so that a and b become parallel?

I really appreciate some help :)

Answer 1

Since `veca` and `vecb` originate form origin ; if they are parallel then `vecb` must be a generated from `veca`
`ie` `vecb` is a scalar multiple of `veca`.

Explanation:

So `vecb = lambdaveca` ; { `lambda` is some scalar}

`rArr[6,t-2]=lambda[-3,2]`

`rArr[6,t-2]=[-3lambda,2lambda]`

`rArr 6=-3lambda rArr lambda = -2`

And now `t-2=2lambda rArr t-2 = -4`

`:.t=-2`

Finally `vecb=[6,-4]` and it is parallel to `veca`.