Further Mathematics 7366: Further Vectors Topical Past Paper Questions

The line $L$ has vector equation $$ \mathbf{r}=\left[\begin{array}{c}4\\ -7\\ 0\end{array}\right]+\lambda\left[\begin{array}{c}-9\\ 1\\ 3\end{array}\right] $$ Give the equation of $L$ in Cartesian form. Tick (✓) one box. [1 mark] $$ \frac{x+4}{-9}=\frac{y-7}{1}=\frac{z}{3} $$ $$…

The two vectors a and b are such that a.b = 0 State the angle between the vectors a and b Circle your answer. [1 mark] 0° 45° 90° 180°

The lines $l_{1}$ and $l_{2}$ have equations $$ \boldsymbol{l}_{1}:\mathbf{r}=\begin{bmatrix}3\\ 1\\ -2\end{bmatrix}+\lambda\begin{bmatrix}3\\ -4\\ 1\end{bmatrix} $$ $$ \begin{array}{l l } l_{2}:\mathbf{r}=\left[\begin{array}{c} {-12}\\{a}\\{-3} \end{array}\right]+\mu\left[\begin…