Mathematics Pure WMA11: Vectors Topical Past Paper Questions

With respect to a fixed origin $O$, the line $l_{1}$ has equation $$ \mathbf{r}=\begin{pmatrix}-3\\0\\5\end{pmatrix}+\lambda\begin{pmatrix}2\\1\\-3\end{pmatrix} $$ where $\lambda$ is a scalar parameter. The point $P$ lies on $l_{1}$ Given that $P$ is the point on $l_{1}$ that is…

Relative to a fixed origin $O$, - the point $A$ has position vector $\mathbf{i} + 2\mathbf{j} - 3\mathbf{k}$ - the point $B$ has position vector $5\mathbf{i} + 2\mathbf{j} + \mathbf{k}$ The line $l$ passes through $A$ and $B$. (a) Write down a vector equation for $l$ (2) Given al…

With respect to a fixed origin $O$, the line $l_{1}$ is given by the equation $$ \mathbf{r}=\mathbf{i}+2\mathbf{j}+5\mathbf{k}+\lambda(8\mathbf{i}-\mathbf{j}+4\mathbf{k}) $$ where $\lambda$ is a scalar parameter. The point $A$ lies on $l_{1}$ Given that $ |\overrightarrow{OA}| =…