Relative to the origin $O$, two points $A$ and $B$ have position vectors given by \(\mathbf{a}

Question

Relative to the origin $O$, two points $A$ and $B$ have position vectors given by $\mathbf{a}=3\mathbf{i}+\mathbf{j}+3\mathbf{k}$ and $\mathbf{b}=5\mathbf{i}-4\mathbf{j}+3\mathbf{k}$ respectively. Find the length of the projection of $\overrightarrow{OA}$ on $\overrightarrow{OB}$.[2] Hence, or otherwise, find the position vector of the point $C$ on $OB$ such that $AC$ is perpendicular to $OB$.[2] Find a vector equation of the reflection of the line $AB$ in the line $AC$.[3]

Accepted Answer

(i) $2\sqrt2\text{ units}$. (ii) $\mathbf c=\frac25(5,-4,3)=(2,-\frac85,\frac65)$. (iii) $\mathbf r=(3,1,3)+\mu(20,1,18)$, $\mu\in\mathbb R$.

2010 ACJC P1 Q9

2010 ACJC P1 Q9

Video Solution:

Solution:

Solution locked