How do you find the cross product and verify that the resulting vectors are perpendicular to the given vectors #<5,2,3>times<-2,5,0>#?

1 Answer
Narad T.
Oct 28, 2016

The cross product is #〈-15,-6,29〉#

Explanation:

The cross product of 2 vectors #vecu=〈u_1,u_2,u_3〉# and #vecv=〈v_1,v_2,v_3〉# is given by

#vecu#x#vecv# #=〈u_2v_3-u_3v_2,u_3v_1-u_1v_3,u_1v_2-u_2v_1〉#
This vector is perpendicular to #vecu# and #vecv#

So the cross product of #〈5,2,3〉# and #〈-2,5,0〉# is #〈-15,-6,29〉#

Verification by making the dot product
#〈5,2,3〉.〈-15,-6,29〉=-75-12+87=0#
and #〈-2,5,0〉.〈-15,-6,29〉=30-30+0=0#

As both dot products are #=0# so the vector is perpendicular to the other 2 vectors

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