What is the dot product of $< - 6, 4, 2 >$ $<-6,4,2 >$ and $< 7, 1, 0 >$ $<7,1,0 >$ ?

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Answer 1 · 2018-04-20T12:38:17

The dot product is $= - 38$ $=-38$

The dot product of $2$ $2$ vectors

$\to a = < a, b, c >$ $veca= < a,b, c>$

and

$\to b = < d, e, f >$ $vecb= < d,e, f>$

is

$\to a . \to b = < a, b, c > . < d, e, f >$ $veca . vecb =< a,b, c> . < d,e, f>$

$= (a \times d) + (b \times e) + (c \times f)$ $=(axxd)+(bxxe)+(cxxf)$

So,

The dot product is

$= < - 6, 4, 2 > . < 7, 1, 0 >$ $=<-6, 4, 2> . <7,1,0>$

$= (- 6 \times 7) + (4 \times 1) + (2 \times 0)$ $=(-6xx7)+(4xx1)+(2xx0)$

$= - 42 + 4 + 0$ $=-42+4+0$

$= - 38$ $=-38$

What is the dot product of <-6,4,2 > <−6,4,2><-6,4,2 > and <7,1,0 > <7,1,0><7,1,0 > ?