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

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Answer 1 · 2018-07-26T05:59:47

The dot product is $= 23$ $=23$

The dot product of $2$ $2$ vectors

$\to a = < x_{1}, x_{2}, x_{3} >$ $veca= < x_1,x_2,x_3>$

and

$\to b = < y_{1}, y_{2}, y_{3} >$ $vecb= < y_1,y_2,y_3>$

is

$\to a . \to b = < x_{1}, x_{2}, x_{3} > . < y_{1}, y_{2}, y_{3} >$ $veca.vecb = < x_1,x_2,x_3> . < y_1,y_2,y_3>$

$= x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3}$ $=x_1y_1+x_2y_2+x_3y_3$

Here the vectors are

$\to a = < 2, 4, 7 >$ $veca = <2,4,7>$ and $\to b = < 1, - 7, 7 >$ $vecb = <1,-7,7>$

The dot product is

$< 2, 4, 7 > . < 1, - 7, 7 > = 2 \cdot 1 + 4 \cdot (- 7) + 7 \cdot 7$ $<2,4,7> . <1,-7,7> = 2*1+4*(-7)+7*7$

$= 2 - 28 + 49$ $=2-28+49$

$= 23$ $=23$

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