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