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how would i go about finding a vector that intersects both lines and then finding another line parallel to that vector? help would be much appreciated

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If so, then it is parallel to the vector going from (0, 0, 0) to (9, 6, 0). If not, then it is not parallel.

- #1

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how would i go about finding a vector that intersects both lines and then finding another line parallel to that vector? help would be much appreciated

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You cannot add 960 + t(0,1,-1) since you cannot add a scalar and a vector meaningfully.

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Before offering more help, let's let the OP respond with an attempt at solving the problem.

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general equation for line 1 x-y+z=0, parametric equation x=s y=2s z=s

general equation for line 2 x+y+z=15, parametric equation x=9 y=6+t z=-t

then created a line with the vector (1,-1,1) going through the origin.

x =(0,0,0) +v(1,-1,1)

therefor general equation is x+2y+z=0, parametric x=v y=-v z=v

crossing of line 1 and line 3

s+4s+s=0

6s=0

s=0

therefore x=0 y=0 z=0

crossing of line 2 and line 3

v-v+v=15

v=15

therefore x=15 y=-15 z=15

so the third line crosses line one at (0,0,0) and line 2 and (15,-15,15)

is this correct?

appreciate all the help

- #6

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Your general equations above are equations of planes, not lines. Your parametric equations represent the lines, though.jonney said:here is what i have come up with is this right

general equation for line 1 x-y+z=0, parametric equation x=s y=2s z=s

general equation for line 2 x+y+z=15, parametric equation x=9 y=6+t z=-t

BTW, in your original post you said

Without commas, the 960 part was confusing to several posters.jonney said:... x=(960)+t(0,1,-1)

jonney said:then created a line with the vector (1,-1,1) going through the origin.

x =(0,0,0) +v(1,-1,1)

therefor general equation is x+2y+z=0, parametric x=v y=-v z=v

crossing of line 1 and line 3

s+4s+s=0

6s=0

s=0

therefore x=0 y=0 z=0

crossing of line 2 and line 3

v-v+v=15

v=15

therefore x=15 y=-15 z=15

so the third line crosses line one at (0,0,0) and line 2 and (15,-15,15)

is this correct?

appreciate all the help

All you need to do is find one point on each line, and then construct a vector from one point to the other. By inspection, (0, 0, 0) is a point on line 1, and (9, 6, 0) is a point on line 2.

Now, form a vector from one point to the other, and then find the equation of the line with this direction that goes through, say, (0, 0, 0). That's what I would do.

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I got x = (0,0,0)+t(9,6,0) for the vector equation of the line does this look right.

also sorry about the confusion on the (960) when it should have been (9,6,0).

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