WEBVTT
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If vector 𝐀 is equal to 𝐢 plus 𝐣 plus 𝐤, vector 𝐁 is equal to 𝐢 minus two 𝐣 plus three 𝐤, and vector 𝐂 equals negative 𝐢 minus 𝐣 plus 𝐤, find 𝐀 plus 𝐁 minus 𝐂.
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In order to add or subtract vectors written in terms of their 𝐢, 𝐣, and 𝐤 unit vectors, we simply add or subtract the corresponding components.
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We can begin with the 𝐢-components.
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We have 𝐢 plus 𝐢 minus negative 𝐢.
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𝐢 plus 𝐢 is equal to two 𝐢.
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And subtracting negative 𝐢 from this gives us three 𝐢.
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For the 𝐣-components, we need to add 𝐣 and negative two 𝐣 and then subtract negative 𝐣.
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𝐣 plus negative two 𝐣 is equal to negative 𝐣.
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Subtracting negative 𝐣 from this gives us zero.
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Finally, we have the 𝐤-components.
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We need to add 𝐤 and three 𝐤 and then subtract 𝐤.
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This is equal to three 𝐤.
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Vector 𝐀 plus vector 𝐁 minus vector 𝐂 is equal to three 𝐢 plus zero 𝐣 plus three 𝐤.
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This can be simplified to three 𝐢 plus three 𝐤.
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If vector 𝐀 is equal to 𝐢 plus 𝐣 plus 𝐤, vector 𝐁 is equal to 𝐢 minus two 𝐣 plus three 𝐤, and vector 𝐂 is equal to negative 𝐢 minus 𝐣 plus 𝐤, then 𝐀 plus 𝐁 minus 𝐂 is equal to three 𝐢 plus three 𝐤.