Question Type 2: Verifying if a point lies on a specific line Exercises

Determine whether the point $(5,3,1)$ lies on the line given by rac{x-2}{3}=rac{y+1}{4}=rac{z-5}{-2}.

Check whether the origin $(0,0,0)$ lies on the line

Determine whether $(0,-2,3)$ lies on the vector line $\mathbf r=\langle1,0,2\rangle+t\langle2,-2,1\rangle.$

Determine whether the point $(4,-1,2)$ lies on the line rac{x}{2}=rac{y+1}{-3}=rac{z-5}{4}.

Check if the point $(-1,4,7)$ lies on the parametric line

Does the point $(6,0,3)$ lie on the line rac{x-1}{5}=rac{y+2}{-2}=rac{z-3}{1}?

Does the point $(2,5,-1)$ lie on the line through $(0,1,-2)$ and $(4,3,2)$?

Determine whether $(8,-7,14)$ lies on the line

Check if $(1,-5,9)$ lies on the line given in vector form $\mathbf r=\langle3,-2,1\rangle+t\langle2,1,4\rangle.$

Does the point $P(7,10,-5)$ lie on the line through $A(1,2,3)$ and $B(4,6,-1)$?

Verify if $(-8,0,10)$ lies on the line

Determine whether the point $(10,-4,6)$ lies on the line passing through $(2,5,-1)$ and parallel to the vector $\langle4,-3,2\rangle$.