Question

Does the line (x-7)/3=(y+8)/6=(z+4)/5 and the point P(10,-2,1) determine a plane? How would I answer this?

Answer 1

\[\frac{ x-7 }{ 3 }= \frac{ y+8 }{ 6 }=\frac{ z+4 }{ 5 }\]

Answer 2

does the given point lie on the line ?

Answer 3

it doesn't say, but i think it does

Answer 4

simply plugin the given point into the given equaiton of line and see if it satisfies

Answer 5

ok I did and they all equal to each other. That means it does determine a plane?

Answer 6

Nope that means the given point lies on the given line

Answer 7

so the line and point just form a line

they dont realize a plane

Answer 8

you need 3 noncollinear points for a plane

Answer 9

oh ok thanks!

Answer 10

yw