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Question

# How do we multiply vectors?

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Solution

## 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

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