WEBVTT
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Given vectors 𝐀 equal to zero, two, negative nine and vector 𝐁 equal to one, three, negative four, express five 𝐀 minus three 𝐁 in terms of the standard unit vectors 𝐢, 𝐣, and 𝐤.
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In order to answer this question, we firstly need to multiply vector 𝐀 by the scalar five and vector 𝐁 by the scalar three.
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When multiplying a vector by a scalar, we simply multiply each of the components by that scalar.
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Five multiplied by vector 𝐀 is therefore equal to five multiplied by the vector zero, two, negative nine.
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This is equal to zero, 10, negative 45.
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To find the vector three 𝐁, we multiply the vector one, three, negative four by the scalar three.
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This is equal to three, nine, negative 12.
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Our next step is to subtract these two vectors.
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We do this by subtracting the corresponding components.
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Zero minus three is equal to negative three.
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10 minus nine is equal to one.
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Finally, negative 45 minus negative 12 is the same as negative 45 plus 12, which equals negative 33.
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Five 𝐀 minus three 𝐁 is equal to the vector negative three, one, negative 33.
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We are asked to write our answer in terms of the standards unit vectors.
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We can do this by recalling that the vector with components 𝑥, 𝑦, and 𝑧 can be written as 𝑥 multiplied by 𝐢 hat plus 𝑦 multiplied by 𝐣 hat plus 𝑧 multiplied by 𝐤 hat.
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The vector negative three, one, negative 33 is therefore equal to negative three 𝐢 plus 𝐣 minus 33𝐤.
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This is the vector five 𝐀 minus three 𝐁 written in terms of the standard unit vectors.