Question Video: Subtracting Vectors in Component Form and Identifying the Resultant on a Grid Physics

Consider the two vectors 𝐀 and 𝐁. 𝐀 = βˆ’2𝐒 βˆ’ 8𝐣 and 𝐁 = 3𝐒 βˆ’ 9𝐣. Which of the five vectors shown in the diagram is equal to 𝐀 βˆ’ 𝐁?

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Video Transcript

Consider the two vectors 𝐀 and 𝐁. 𝐀 is equal to negative two 𝐒 minus eight 𝐣, and 𝐁 is equal to three 𝐒 minus nine 𝐣. 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 find the resultant vector 𝐀 minus 𝐁 by subtracting the components of 𝐁 from the components of 𝐀. For the horizontal component, we have negative two minus three, which is equal to negative five. And for the vertical component, we have negative eight minus negative nine, which is equal to negative eight plus nine, or plus one.

We can then draw the resultant vector 𝐀 minus 𝐁 onto our diagram by starting at the origin and going negative one, two, three, four, five in the horizontal direction and positive one in the vertical direction. And there we find the vector 𝐓. So 𝐀 minus 𝐁 is equal to the vector 𝐓.

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