Question Type 2: Verifying if a point lies on a line or not Exercises

Determine whether the point $(2,-3,4)$ lies on the line defined by $x=5-t,\;y=-1-2t,\;z=1+3t$.

Determine whether the point $(-1,4,0)$ lies on the line given in parametric form by $\mathbf{r} = \begin{pmatrix} 2 \\ 1 \\ -3 \end{pmatrix} + t \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix}$.

Determine if the point $(5,-1,7)$ lies on the line: $\frac{x+1}{3}=\frac{y-4}{-2}=\frac{z-1}{5}$

Show that the point $(4, 6, 8)$ lies on the line passing through the origin $(0, 0, 0)$ and the point $(2, 3, 4)$.

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

Determine whether $(7,-1,5)$ lies on the line $\frac{x-3}{4}=\frac{y+2}{-1}=\frac{z-1}{2}$.

Determine whether $Q(3,3,3)$ lies on the line given by $\mathbf r=(1,2,1)+\lambda(2,1,4)$

Verify whether $P(0,3,-2)$ lies on the line through $A(2,1,0)$ and $B(-1,4,2)$

Determine whether $(-3,-1,7)$ lies on the line $\frac{x+1}{-2}=\frac{y-3}{1}=\frac{z-5}{4}$

Determine whether the point $(4,0,5)$ lies on the parametric line $x=1+3t,\;y=-2+t,\;z=2-2t$.

Verify whether the point $(2,1,3)$ lies on the line given by $\frac{x-5}{2}=\frac{y-1}{3}=z$.