### Video Transcript

Given the vector ๐ฏ equals seven, two and the vector ๐ฎ equals three, six, find the dot product of vectors ๐ฎ and ๐ฏ.

We recall that if vector ๐ฎ has components ๐ข sub ๐ฅ and ๐ข sub ๐ฆ and vector ๐ฏ has components ๐ฃ sub ๐ฅ and ๐ฃ sub ๐ฆ, then the dot product of vectors ๐ฎ and ๐ฏ is equal to ๐ข sub ๐ฅ, ๐ฃ sub ๐ฅ plus ๐ข sub ๐ฆ, ๐ฃ sub ๐ฆ. 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 doesnโt matter in which order we multiply the vectors. ๐ฎ dot ๐ฏ is equal to ๐ฏ dot ๐ฎ.