What is the dot product of $< - 8, 4, 2 >$ $<-8,4,2 >$ and $< - 3, 1, 6 >$ $<-3,1,6 >$ ?

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Answer 1 · 2016-10-29T03:19:03

$= 40$ $=40$

It is easier to visualise what is happening if you write the vectors in vertical form. (imagine brackets around the stacks of numbers)

$(- 8)$ $(-8)$ $(- 3)$ $" "(-3)$
$(4)$ $" "(4)$ $\cdot$ $*$ $(1)$ $" "(1)$
$(2)$ $" "(2)$ $(6)$ $" "(6)$

now we take each of the rows, multiply them, and then add the products together,

$((- 8) \cdot (- 3)) + ((4) (1)) + ((2) (6))$ $((-8)*(-3))+((4)(1))+((2)(6))$

$= 24 + 4 + 12$ $=24+4+12$

$= 40$ $=40$

What is the dot product of <-8,4,2 > <−8,4,2><-8,4,2 > and <-3,1,6 > <−3,1,6><-3,1,6 > ?