What is $| | < 7, 3, - 1 > - < - 2, 5, 3 > | |$ $|| <7, 3, -1> - < -2 , 5, 3 > ||$ ?

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Answer 1 · 2017-01-10T03:42:21

$| | < 7, 3, - 1 > - < - 2, 5, 3 > | | = \sqrt{101}$ $|| < 7,3,-1 > - < -2,5,3 >|| =sqrt(101)$ .

See below.

To subtract two vectors $\to a$ $veca$ and $\to b$ $vecb$ :

$\to a - \to b = < a_{1} - b_{1}, a_{2} - b_{2}, a_{3} - b_{3} >$ $veca-vecb=< a_1-b_1,a_2-b_2, a_3-b_3 >$

The result is a vector, $\to c$ $vecc$ .

The magnitude of the resultant vector is then given by:

$∣ ∣ \to c ∣ ∣ = \sqrt{{(c_{1})}_{1}^{2} + {(c_{2})}_{2}^{2} + {(c_{3})}_{3}^{2}}$ $|vecc|=sqrt((c_1)^2+(c_2)^2+(c_3)^2)$

Given $\to a = < 7, 3, - 1 >$ $veca=< 7,3,-1 >$ and $\to b = < - 2, 5, 3 >$ $vecb=< -2,5,3 >$ ,

$\to a - \to b = < 7 - (- 2), 3 - 5, - 1 - 3 >$ $veca-vecb= < 7-(-2), 3-5, -1-3 >$

$= < 9, - 2, - 4 >$ $=< 9, -2, -4 >$

The magnitude is then:

$∣ ∣ \to c ∣ ∣ = \sqrt{9^{2} + {(- 2)}^{2} + {(- 4)}^{2}}$ $|vecc|=sqrt(9^2+(-2)^2+(-4)^2)$

$= \sqrt{101}$ $=sqrt(101)$

What is ||<7,3,−1>−<−2,5,3>|||| <7, 3, -1> - < -2 , 5, 3 > ||?