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Video: Determining the Dot Product between Given Vectors

Alex Cutbill

Given that 𝐀 = 〈−6, −3, 5〉 and 𝐁 = 〈7, −4, −1〉, determine 𝐀 ⋅ 𝐁.

01:06

Video Transcript

Given that the vector 𝐀 has components negative six, negative three, five and the vector 𝐁 has components seven, negative four, negative one, determine the dot product of 𝐀 and 𝐁, 𝐀 dot 𝐁.

We wanted to find the dot product of 𝐀 and 𝐁, and we’re going to use the component forms of the vectors. So here, we’ve just substituted in the component forms. And actually, given the component forms of two vectors, it’s very easy to find that dot product. It is the product of the first components plus the product of the second components plus the product of the third components. And if the vectors had four or five or six or so on components, we would just continue this process, adding up the products of components until we run out of components.

Evaluating these products, we get negative 42 plus 12 minus five which is negative 35.