Answer:
The resultant of the dot product of two vectors is:
[tex]v\cdot w=22[/tex]
Step-by-step explanation:
We are asked to find the dot product of the two vectors v and w.
The vectors are given by:
r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>
This means that in the vector form they could be written as follows:
[tex]r=8\hat i+8\hat j -6\hat k\\\\v=3\hat i-8\hat j -3\hat k\\\\w=-4\hat i-2\hat j -6\hat k[/tex]
Hence, the dot product of two vectors is the sum of the product of the entries corresponding to each direction component.
i.e. the x-component get multiplied to each other, y-component get multiplied to each other and so happens with z.
Hence, the dot product of v and w is calculated as:
[tex]v\cdot w=3\times (-4)-8\times (-2)-3\times (-6)\\\\i.e.\\\\v\cdot w=-12+16+18\\\\i.e.\\\\v\cdot w=22[/tex]
