### Video Transcript

True or false: vectors π equals
two, one and π equals six, three are parallel. Option (A) true or option (B)
false.

In this question, weβre given
information about two vectors π and π, and weβre asked to work out if these two
vectors are parallel. We can recall that two vectors are
parallel if they are scalar multiples of each other. If vectors π and π are parallel,
then we could write that vector π is equal to π times vector π for some scalar
quantity π, where π is not equal to zero. Given the information about vectors
π and π, then we can fill these into this equation and check if itβs valid. You might notice that vector π is
a nice multiple of vector π. But itβs worth checking the π₯- and
π¦-components separately.

Evaluating the π₯-components, weβd
have two is equal to six π. Dividing both sides by six would
give us two-sixths is equal to π. Simplifying would give us a third
equals π or π is equal to one-third. In order for these vectors to be
parallel, then when we evaluate the π¦-components, we need to get the same value of
π. So, letβs check. When we evaluate the π¦-components,
we get that one is equal to three π. Dividing both sides by three, weβd
get that one-third is equal to π which, of course, means that π is equal to
one-third. We can then say that vector π does
equal π times vector π because we can write that vector π is equal to one-third
times vector π. We could therefore give the answer
true since the statement βvectors π and π are parallelβ is true.

One alternative way to answer this
question would be to represent these vectors on a diagram. Vector π is given as two, one, and
vector π is given as six, three. We can see visually that vectors π
and π are parallel, confirming the answer that the statement is true.