Video Transcript
Given that π is the vector two,
negative one, express the vector π in terms of the unit vectors π’ and π£.
In this question, weβre given a
vector π and itβs given in terms of its components. We need to write vector π in terms
of the unit vectors π’ and π£. To answer this question, weβre
first going to need to recall what it means to represent a vector in terms of its
components. We recall a vector is an object
with magnitude and direction, and thereβs a lot of different ways we can think about
magnitude and direction. And thereβs a lot of different ways
we can express this. This is the main reason why we have
lots of different ways of expressing vectors.
One way of thinking about magnitude
and direction is to think about the magnitude in specific directions. For example, the vector π, π is
telling us we have a magnitude of size π in the direction of vector π’ and a
magnitude of size π in the direction of vector π£ because π’ and π£ are our unit
directional vectors. We need both of these pieces of
information to fully determine the magnitude and direction of our vector. In the question, weβre given the
vector π which is the vector two, negative one. So by applying this, we must have
that this is the vector two π’ plus negative one times π£. And multiplying a vector by
negative one is the same as subtracting this vector. So we can simplify this to get our
final answer of two π’ minus π£.
