How do you find a vector parametric equation for the line through the points P= (0,4,-3) and Q=(-5,4,1)?

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Answer 1 · 2017-01-15T14:05:29

# vec(r) = ( (0),(4), (-3) ) + lamda ( (-5),(0), (4) ) #

In vector notation we have;

We have

# vec(OP) = ( (0),(4), (-3) ) # and # vec(OQ) = ( (-5),(4), (1) ) #

And so the direction of the line is given by:

# vec(PQ) = ( (-5),(4), (1) ) - ( (0),(4), (-3) ) = ( (-5),(0), (4) ) #

And so the vector equation of the line is

# vec(r) = ( (0),(4), (-3) ) + lamda ( (-5),(0), (4) ) #