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

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

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Answer 1 · 2016-01-03T16:52:53

The dot product of two three dimensional vectors is defined as

$a \cdot b = a_{x} \cdot b_{x} + a_{y} \cdot b_{y} + a_{z} \cdot b_{z}$ $a*b=a_x*b_x+a_y*b_y+a_z*b_z$

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

hence

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

Answer 2 · 2016-01-03T16:55:14

$- 19$ $-19$

Explanation:

To do the dot product, you multiply together the corresponding components, and then sum the results. In general:
$(a_{1}, a_{2}, a_{3}) \cdot (b_{1}, b_{2}, b_{3}) = (a_{1} b_{1} + a_{2} b_{2} + a_{3} b_{3})$ $(a_1, a_2, a_3)*(b_1, b_2, b_3)=(a_1b_1+a_2b_2+a_3b_3)$

So in your case:

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

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

2 Answers

Explanation:

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

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