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

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

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

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

Check if the point $(-1,4,0)$ lies on the line given in parametric form by $\mathbf r=(2,1,-3)+t(1,2,1)$

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

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

Is the point $(-2,5,1)$ on the line $\displaystyle\frac{y-2}{2}=\frac{z+1}{-3}=\frac{x+4}{1}$? Verify.

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 $B(-1,4,2)$

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

Verify whether $(4,6,8)$ lies on the line passing through $(0,0,0)$ and $(2,3,4)$