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Question Video: Finding the Dot Product of Two Vectors Mathematics • 12th Grade

Given the vector 𝐯 = 〈7, 2〉 and the vector 𝐮 = 〈3, 6〉, 𝐮 ⋅ 𝐯.

01:24

Video Transcript

Given the vector 𝐯 equals seven, two and the vector 𝐮 equals three, six, find the dot product of vectors 𝐮 and 𝐯.

We recall that if vector 𝐮 has components 𝑢 sub 𝑥 and 𝑢 sub 𝑦 and vector 𝐯 has components 𝑣 sub 𝑥 and 𝑣 sub 𝑦, then the dot product of vectors 𝐮 and 𝐯 is equal to 𝑢 sub 𝑥, 𝑣 sub 𝑥 plus 𝑢 sub 𝑦, 𝑣 sub 𝑦. We find the sum of the products of the corresponding components.

In this question, we need to find the dot product of vectors three, six and seven, two. This is equal to three multiplied by seven plus six multiplied by two, which simplifies to 21 plus 12, giving us a final answer of 33. The dot product of vectors three, six and seven, two is 33.

We note that this is a scalar quantity. And since multiplication is commutative, it doesn’t matter in which order we multiply the vectors. 𝐮 dot 𝐯 is equal to 𝐯 dot 𝐮.

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