Question

How do we multiply vectors?

Answer 1

multiplication of the vector is normal multiplication as you do ussual. but vector multiplication is two type The Dot Productlet
dot product of two vector, result is scalar
let two vector
A= 2i +2j +5k
and B= 5i+5j+4k
now dot product A.B =( 2i +2j +5k).(5i+5j+4k)
A.B=(2*5)i.i +(2*5)i.j+(2*4)i.k+(2*5)j.i+(2*5)j.j+(2*4)j.k+(5*5)k.i+(5*5)k.j+(5*4)k.k

for dot product remember

i.i=j.j=k.k=1
i.j=j.k=k.i=0

A.B=10+10+20=40
A.B=40

The Cross Product result is vector
Use the formula AxB= to determine the cross product of vectors a and b.

let two vector
A= 2i +2j +5k
and B= 5i+5j+4k
AxB =( 2i +2j +5k)x(5i+5j+4k)
=(2*5)ixi +(2*5)ixj+(2*4)ixk+(2*5)jxi+(2*5)jxj+(2*4)j x k+(5*5)kxi+(5*5)kxj+(5*4)kxk

but in cross product
i.i=j.j=k.k=0
ixj=k
jxk=i
kxi=j
now for practive do yourself find AxB by just putting above value