What is the cross product of #<7, 5 ,6 ># and #<3 ,5 ,-6 >#?

1 Answer
Jan 5, 2017

Answer:

The answer is #=〈-60,60,20〉#

Explanation:

The cross product of 2 vectors, #〈a,b,c〉# and #d,e,f〉#

is given by the determinant

#| (hati,hatj,hatk), (a,b,c), (d,e,f) | #

#= hati| (b,c), (e,f) | - hatj| (a,c), (d,f) |+hatk | (a,b), (d,e) | #

and # | (a,b), (c,d) |=ad-bc#

Here, the 2 vectors are #〈7,5,6〉# and #〈3,5,-6〉#

And the cross product is

#| (hati,hatj,hatk), (7,5,6), (3,5,-6) | #

#=hati| (5,6), (5,-6) | - hatj| (7,6), (3,-6) |+hatk | (7,5), (3,5) | #

#=hati(-30-30)-hati(-42-18)+hatk(35-15)#

#=〈-60,60,20〉#

Verification, by doing the dot product

#〈-60,60,20〉.〈7,5,6〉=-420+300+120=0#

#〈-60,60,20〉.〈3,5,-6〉=-180+300-120=0#

Therefore, the vector is perpendicular to the other 2 vectors