# Thread: Vector parallel to plane? Goes through origin?

1. ## Vector parallel to plane? Goes through origin?

Is the vector parallel to the plane? Are there values for $\lambda$ and $\mu$ such that $\lambda<4, 5, 2>+ \mu<-5, 5, 3>= <5, -24, 50>$?
Is the vector in the plane? What does that mean? A vector is "movable" and does not actually lie in any plane. Are you interpreting <5,-24,50> as the vector from (0, 0, 0) to (5, -24, 50)? If so are there values for $\lambda$ and $\mu$ such that $\lambda<4, 5, 2>+ \mu<-5, 5, 3>= <5, -24, 50>$ and are there values for $\lambda$ and $\mu$ such that $\lambda<4, 5, 2>+ \mu<-5, 5, 3>= <0, 0, 0>$?