Video Transcript
Using the rectangular prism below,
decide which of the following is skew to the line πΆπΊ. Option (A) the line π»πΊ, option
(B) the line π·πΆ, option (C) the line πΈπ», option (D) the line πΉπ΅, or option (E)
the line πΆπ΅.
We can recall that skew lines are
lines that do not intersect and are not parallel. They are noncoplanar, which means
they donβt lie on the same plane, and therefore they can only exist in three
dimensions. So, letβs highlight the line πΆπΊ
on the diagram. Because weβre looking for a line
which is skew to the line πΆπΊ, then that line canβt be parallel to the line πΆπΊ,
nor can it intersect this line. There are in fact a few different
lines which can be said to be skew to the line πΆπΊ in this diagram.
Firstly, we have the line π΄π·. The line πΈπ» is also skew to the
line πΆπΊ, so is the line π΄π΅ and the line πΈπΉ. So, there are four different lines
on this diagram that we can identify as being skew to the line πΆπΊ. However, only one of them appears
in the given list of answer options. So, our answer is that given in
option (C). Itβs the line πΈπ».
However, before we finish with this
question, we can double-check the answer options to see what relationship those
lines have with the line πΆπΊ. Answer option (A) gives the line
π»πΊ. However, this line will be
perpendicular to the line πΆπΊ because they lie on the same plane and they intersect
at 90 degrees. In the same way, in option (B), the
line π·πΆ we know will also intersect at 90 degrees. π·πΆ and πΆπΊ are two perpendicular
lines.
In option (D), the line πΉπ΅ can be
seen as parallel to the line πΆπΊ. And finally, the line πΆπ΅ given in
option (E) will also be perpendicular to the line πΆπΊ. As none of these other four options
are lines which are skew to the line πΆπΊ, then there is just one possible
answer. Itβs the line πΈπ».