What is #|| <4, 5, -7 > - < 9, -2, 1 > ||#?

1 Answer
Dec 28, 2016

Answer:

#|< 4,5,-7 > - < 9,-2,1 >|=sqrt(138)#

Explanation:

Given #veca=< 4,5,-7 ># and #vecb=< 9,-2,1 >#, we can subtract #vecb# from #veca# by subtracting the components of #vecb# from those of #veca#.

#< 4,5,-7 > - < 9,-2,1 >#

#=> < (4-9), (5-(-2)), (-7-1) >#

#=>< -5, 7, -8 >#

Let's call this new vector #vecc#, where #vecc=< c_x,c_y,c_z >#. The magnitude of #vecc# is then given by:

#|vecc|=sqrt((c_x)^2+(c_y)^2+(c_z)^2)#

#=>|vecc|=sqrt((-5)^2+(7)^2+(-8)^2)#

#=>|vecc|=sqrt(25+49+64)#

#=>|vecc|=sqrt(138)#

#:.|< 4,5,-7 > - < 9,-2,1 >|=sqrt(138)#