Is the line through (-4, -6, 1) and (-2, 0 , -3) parallel to the line through (10, 18, 4) and (5, 3, 14) ?

Question

chupacabraj · Answer

How?

benji · Answer

Alright, when we need to find an equation we need two things: a point, and a slope. So when we are given two sets of points, we need to find the slope using them, you do this with the equation $$m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1}}$$After you find the slope you can use the point-slope formula to find your equation; the point slope formula is $$y-y _{1}=m(x-x _{1})$$ You can choose any of the two pairs to plug into your point slope form, start by finding the slope what do you get??

mathmale · Answer

Note that this problem is one in 3-dimensional space.  Have you taken that into account?  If this is a course in vector calculus, find the direction vectors of the two lines and compare them.  If the same, the 2 lines are parallel; otherwise, they are not parallel.