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

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Answer 1 · 2017-01-10T03:42:21

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

See below.

To subtract two vectors $veca$ and $vecb$ :

$veca-vecb=< a_1-b_1,a_2-b_2, a_3-b_3 >$

The result is a vector, $vecc$ .

The magnitude of the resultant vector is then given by:

$|vecc|=sqrt((c_1)^2+(c_2)^2+(c_3)^2)$

Given $veca=< 7,3,-1 >$ and $vecb=< -2,5,3 >$ ,

$veca-vecb= < 7-(-2), 3-5, -1-3 >$

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

The magnitude is then:

$|vecc|=sqrt(9^2+(-2)^2+(-4)^2)$

$=sqrt(101)$

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