How do you find a vector equation and parametric equations for the line segment that joins P to Q where P(-7, 2, 0), Q(3, -1, 2)?

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Answer 1 · 2016-08-13T23:00:43

#= ((-7),(2),(0)) + t \ ((10),(-3),(2))#

you want line #vec l# where:

#vec l = vec(OP) + t \ vec (PQ)#

Now #vec (PQ) = vec (PO) + vec (OQ)#

#= - vec (OP) + vec (OQ) #

# = vec (OQ) - vec (OP)#

#= ((3),(-1),(2)) - ((-7),(2),(0)) = ((10),(-3),(2))#

So #vec l = vec(OP) + t \ vec (PQ)#

#= ((-7),(2),(0)) + t \ ((10),(-3),(2))#