WEBVTT
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If the two vectors 𝐀 which is equal to five, negative 10 and 𝐁 which is equal to two, 𝑘 are perpendicular, determine the value of 𝑘.
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We recall that if two vectors 𝐮 and 𝐯 are perpendicular, then their dot or scalar product is equal to zero.
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We can calculate the dot product as follows.
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If vector 𝐮 has components 𝑢 sub one and 𝑢 sub two and vector 𝐯 has components 𝑣 sub one and 𝑣 sub two, then the dot product of 𝐮 and 𝐯 is equal to 𝑢 sub one multiplied by 𝑣 sub one plus 𝑢 sub two multiplied by 𝑣 sub two.
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In this question, we need to calculate the dot product of vector 𝐀 and vector 𝐁.
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This is equal to five multiplied by two plus negative 10 multiplied by 𝑘.
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This in turn simplifies to 10 minus 10𝑘.
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As the vectors are perpendicular, this is equal to zero.
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We can then add 10𝑘 to both sides of our equation such that 10𝑘 is equal to 10.
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Finally, dividing both sides of this equation by 10 gives us 𝑘 is equal to one.
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If the two vectors five, negative 10 and two, 𝑘 are perpendicular, then 𝑘 is equal to one.