Given that $u = 3i + 2j$ and $v = 2i + \lambda j $ determine $\lambda$ such that:
(a) $u$ and $v$ are at right angles (this means perpendicular I presume?)
(b) $u$ and $v$ are parallel
Whilst working out the first one, I obtained the value of -3 for $\lambda$. However I am not sure whether this is correct and am not quite sure how to tackle question (b) from this exercise.
What I can't seem to grasp is, how on earth does the value of lambda determine whether these points on the XY plane are parallel or not?
Would the multiple of the two vectors result in a 0 for perpendicular vectors? If it indeed so then the shift-cosine of 0 would give us 90 degrees (indeed perpendicular). But what value would the multiple of both of those vectors require to be in order to be parallel?