What is the dot product of $<5,1,-7>$ and $<8,4,9>$ ?

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What is the dot product of $<5,1,-7>$ and $<8,4,9>$ ?

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Answer 1 · 2016-01-03T16:52:53

The dot product of two three dimensional vectors is defined as

$a*b=a_x*b_x+a_y*b_y+a_z*b_z$

In our case $a=(5,1,-7)$ and $b=(8,4,9)$

hence

$a*b=5*8+1*4-7*9=-19$

Answer 2 · 2016-01-03T16:55:14

$-19$

Explanation:

To do the dot product, you multiply together the corresponding components, and then sum the results. In general:
$(a_1, a_2, a_3)*(b_1, b_2, b_3)=(a_1b_1+a_2b_2+a_3b_3)$

So in your case:

$(5*8)+(1*4)+(-7*9)$
$=40+4-63$
$=-19$

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What is the dot product of $<5,1,-7>$ and $<8,4,9>$ ?

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