How do you find the cross product and verify that the resulting vectors are perpendicular to the given vectors #<4,0,=2>times<-7,1,0>#?

1 Answer
Oct 23, 2016

Answer:

The vector is #〈2,14,4〉#

Explanation:

The cross product of #〈4,0,-2〉xx〈-7,1,0〉# is

#veci##color(white)(aa)##vecj##color(white)(aa)##veck#
#4##color(white)(aaa)##0##color(white)(aa)##-2#
#-7##color(white)(aa)##1##color(white)(aaa)##0#

cross product #=##(veci(0+2)+vecj(-(0-14))+veck(4-0))#

#=〈2,14,4〉#
To check this we do the dot products

#〈2,14,4〉#.#〈4,0,-2〉##=8+0-8=0#

#〈2,14,4〉##〈-7,1,0〉##=-14+14+0=0#

As the dot products are #=0#
So the 3 vectors are perpendicular