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)#