Question 1040746
If the vectors are perpendicular, then the dot product equals zero.
A=(3,0,2)
B=(2,-2,5)
C=(0,2,7)
D=(-2,10,7)
So then,
BA=(2-3,-2-0,5-2)=(-1,-2,3)
BC=(2-0,-2-2,5-7)=(2,-4,-2)
The dot product is,
{{{BA*BC=-1*2+(-2)(-4)+3(-2)}}}
Complete that to verify that the dot product is zero.
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AD=(3-(-2),0-10,2-7)=(5,-10,-5)
AD=5*(1,-2,1)
Similarly for BC,
BC=(2,-4,2)
BC=2*(1,-2,1)
So they are both multiples of the same vector and the ratios of their lengths is equal to the ratio of the multipliers,
{{{AD/BC=5/2}}}