IB Mathematics Applications & Interpretation Question Type 1: Finding Vector Equation of a Line Passing Through Two Points Exercises

Determine if point $N(7,4,1)$ lies on the line defined by the equation

$$\frac{x+1}{4}=\frac{y-2}{-1}=\frac{z-3}{2}$$

Determine whether the point $(4,-2,5)$ lies on the line $$\vec{r}=\left(\begin{array}{c}1\\ 0\\ 2\end{array}\right)+t\left(\begin{array}{c}3\\ -1\\ 1\end{array}\right).$$

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

Express the line $\vec{r}=\left(\begin{array}{c}2\\ -1\\ 3\end{array}\right)+s\left(\begin{array}{c}-5\\ 4\\ 2\end{array}\right)$ in symmetric form.

Find the vector equation of the line passing through the points $P(1,4,3)$ and $Q(-1,2,1)$.

Find the parametric equations of the line $\vec{r}=\left(\begin{array}{c}0\\ 1\\ 6\end{array}\right)+k\left(\begin{array}{c}4\\ 2\\ 1\end{array}\right)$.

Convert the line $\frac{x-3}{1}=\frac{y+2}{-2}=\frac{z-5}{4}$ into vector form.

Find the vector equation of the line joining $E(3,0,1)$ to $F(-1,4,-2)$.

Verify whether $(0,3,4)$ lies on the line through $(2,1,2)$ in direction $(-2,2,3)$.

Find the parametric equations of the line with Cartesian equation $$\frac{x}{2}=\frac{y-3}{3}=\frac{z+1}{-1}$$

Write the vector equation of the line through $C(0,5,-2)$ and $D(-4,1,-6)$.

Determine a vector equation of the line through points $A(2,-1,0)$ and $B(5,2,3)$.