Question Video: Adding Vectors Mathematics

Find the sum of the vectors 𝐀𝐁 = 3𝐢 − 4𝐣 and 𝐂𝐃 = −5𝐢 − 5𝐣.

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Video Transcript

Find the sum of the vectors 𝐀𝐁, which is equal to three 𝐢 minus four 𝐣, and 𝐂𝐃, which is equal to negative five 𝐢 minus five 𝐣.

We are asked to find the sum of the vectors. So we need to add vector 𝐀𝐁 to vector 𝐂𝐃. Vector 𝐀𝐁 is equal to three 𝐢 minus four 𝐣, and vector 𝐂𝐃 is equal to negative five 𝐢 minus five 𝐣. When adding two vectors, we simply add the corresponding components. Three 𝐢 plus negative five 𝐢 is the same as three 𝐢 minus five 𝐢, which gives us negative two 𝐢. Negative four 𝐣 plus negative five 𝐣 is equal to negative nine 𝐣. The sum of the vectors 𝐀𝐁 and 𝐂𝐃 is equal to negative two 𝐢 minus nine 𝐣.

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