Consider the two vectors 𝐀 and 𝐁,
where 𝐀 is equal to eight 𝐢 plus 10𝐣 and 𝐁 is equal to three 𝐢 plus two 𝐣. Calculate 𝐀 minus 𝐁.
In our problem, we are given vector
𝐀 and 𝐁 in unit vector notation. Therefore, we need to remember that
when we subtract vectors in unit vector notation, we need to subtract the individual
components. This means that we’ll subtract the
𝐢’s and separately we’ll subtract the 𝐣’s. We can align the vectors vertically
along with the subtraction sign to make the subtraction of the components
easier. We put hats over our 𝐢 and 𝐣 unit
vectors as we are writing our workout by hand. But in the text form of the
problem, 𝐢 and 𝐣 were bolded to show that they were unit vectors.
We can use the vector 𝐕 to
represent the resultant vector of 𝐀 minus 𝐁. To find our resultant, we start
with the 𝐢-components. Eight 𝐢 minus three 𝐢 is five
𝐢. Then, we subtract the 𝐣’s. 10𝐣 minus two 𝐣 is eight 𝐣. When we subtract two vectors 𝐀 and
𝐁, where 𝐀 is equal to eight 𝐢 plus 10𝐣 and 𝐁 is equal to three 𝐢 plus two 𝐣,
we get a resultant of five 𝐢 plus eight 𝐣.