Vector Derivative and Tangent – Tangent to the curve in a vector representation parallel to a given plane – Exercise 3839

Exercise

Find a point on the curve

$$\vec{r}(t)=t^2\vec{i}+t\vec{j}+5\vec{k}$$

Where the tangent to a curve is parallel to the plain

$$x-6y+4z=3$$

$$M(9,3,5)$$