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

1 Answer
Morgan
Dec 28, 2016

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

Explanation:

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

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

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

=>< -5, 7, -8 >⇒<−5,7,−8>

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

|vecc|=sqrt((c_x)^2+(c_y)^2+(c_z)^2)∣∣→c∣∣=√(cx)2+(cy)2+(cz)2

=>|vecc|=sqrt((-5)^2+(7)^2+(-8)^2)⇒∣∣→c∣∣=√(−5)2+(7)2+(−8)2

=>|vecc|=sqrt(25+49+64)⇒∣∣→c∣∣=√25+49+64

=>|vecc|=sqrt(138)⇒∣∣→c∣∣=√138

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

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