Video Transcript
Consider two vectors π and π. π is equal to two π’ plus three
π£, and π is equal to seven π’ plus five π£. Calculate π plus π.
In this problem, the vectors π and
π have been written in bold to show that theyβre vectors. Since weβre going to be solving
this by hand, we can signify that π and π are vectors by drawing half arrows over
the top. Similarly, the unit vectors π’ and
π£ have been written in bold. When writing these by hand, we draw
a hat over the top to signify that theyβre unit vectors. Whenever weβre adding vectors which
are expressed in unit vector notation, like π and π, we need to remember to add
the π’-components and the π£-components separately.
It can be useful to write the
vectors one above the other with a plus sign so that the π’-components and the
π£-components are vertically aligned. Adding the two vectors π and π
together will give us a vector as a result. We can give this resultant vector a
name. Letβs call it π. To determine the components of π,
we start by adding together the π’-components of π and π. Two π’ plus seven π’ is nine
π’. Next, we add together the
π£-components, and three π£ plus five π£ is eight π£. If vector π is equal to two π’
plus three π£ and vector π is equal to seven π’ plus five π£, then π plus π is
equal to nine π’ plus eight π£.