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

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

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Answer 1 · 2018-03-17T09:41:30

The dot product is $= 0$ $=0$

Explanation:

The dot product of $2$ $2$ vectors $< x_{1}, x_{2}, x_{3} >$ $< x_1,x_2,x_3>$ and $< y_{1}, y_{2}, y_{3} >$ $< y_1,y_2,y_3 >$ is

$< x_{1}, x_{2}, x_{3} > . < y_{1}, y_{2}, y_{3} > = x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3}$ $< x_1,x_2,x_3> .< y_1,y_2,y_3 > = x_1y_1+x_2y_2+x_3y_3$

Therefore,

$< - 1, - 2, 1 > . < - 1, 2, 3 > = (- 1) \cdot (- 1) + (- 2) \cdot (2) + (1) \cdot (3)$ $< -1, -2, 1> .< -1, 2, 3 > = (-1)*(-1)+ (-2)*(2)+(1)*(3)$

$= 1 - 4 + 3$ $=1-4+3$

$= 0$ $=0$

As the dot product is $= 0$ $=0$ , the vectors are orthogonal.

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

1 Answer

Explanation:

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