Video: Subtracting Vectors Using Unit Vectors

Consider the two vectors 𝐀 and 𝐁, where 𝐀 = 8𝐢 + 10𝐣 and 𝐁 = 3𝐢 + 2𝐣. Calculate 𝐀 − 𝐁.

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Video Transcript

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.

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