Question Video: Finding the Sum of Vectors in Component Form and Identifying the Resultant on a Grid

Consider two vectors 𝐀 and 𝐁. 𝐀 = 4𝐒 βˆ’ 9𝐣 and 𝐁 = 1𝐒 βˆ’ 12𝐣. Which of the five vectors shown in the diagram is equal to 𝐀 βˆ’ 𝐁?

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Video Transcript

Consider two vectors 𝐀 and 𝐁. 𝐀 equals four 𝐒 minus nine 𝐣 and 𝐁 equals one 𝐒 minus 12𝐣. Which of the five vectors shown in the diagram is equal to 𝐀 minus 𝐁?

Since we’re given the vectors 𝐀 and 𝐁 in component form, we can calculate 𝐀 minus 𝐁 by subtracting the components of 𝐁 from the components of 𝐀. If we first consider the horizontal components 𝐒, we have four minus one, which is equal to three. And then considering the vertical components 𝐣, we have negative nine minus negative 12, which is equal to negative nine plus 12 or positive three.

We can then add this vector to our diagram by going positive three in the horizontal direction and then positive three in the vertical direction. And there we find vector 𝐐. Therefore, 𝐀 minus 𝐁 is equal to 𝐐.

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