Question

Question #62f79

Answer 1

I presume that you wish to show that `AB _|_BC`

Define the following vectors:

`bb ul(A) = ( (3),(-7.5),(4.5) ); \ \ bb ul(B) = ( (5.5),(-2.5),(5.5) ); \ \ bb ul(C) = ( (10.5),(-5),(5.5) )`

So then:

`bb vec(AB) = ( (5.5),(-2.5),(5.5) ) - ( (3),(-7.5),(4.5) ) = ( (2.5),(5),(1) )`

And:

`bb vec(BC) = ( (10.5),(-5),(5.5) ) - ( (5.5),(-2.5),(5.5) ) = ( (5),(-2.5),(0) )`

And the dot product of these two vectors is:

`bb vec(AB) * bb vec(BC) = ( (2.5),(5),(1) ) * ( (5),(-2.5),(0) ) = 0`

And as the dot product is zero, then `AB _|_BC`