Let #bbx=bbe_1+bbe_2-2bbe_3# and #bby=2bbe_1-bbe_2+bbe_3#,where #bbe_1,bbe_2,bbe_3# are unit vectors. Find #|bbx+2bby|# and #|bbx+bby#|?

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Answer 1 · 2018-02-15T17:20:48

See below.

Assuming that the basis #e_1,e_2,e_3# is orthonormal.

Taking

#x = (1,1,-2)# and #y = (2,-1,1)# we have

#z = x+2y = (1,1,-2)+2 (2,-1,1) = (5,-1,0)#

#abs(z) = sqrt(5^2+1^1+0^2) = sqrt(26) = abs (x+2y)#

Analogously

#z = x + y = (1,1,-2)+ (2,-1,1) = (3,0,-1)# and then

#absz = sqrt(3^2+0^2+1^2) = sqrt10 = abs(x+y)#