The position vectors of two points $A$ and $B$ are $(\mathbf{i}-3\mathbf{j}+2\mathbf{k})$ and

Question

The position vectors of two points $A$ and $B$ are $(\mathbf{i}-3\mathbf{j}+2\mathbf{k})$ and $(4\mathbf{i}+2\mathbf{k})$ respectively. Given that point $C$ is on line $AB$ and $9$ units away from $B$, find the possible position vectors of $C$.

Accepted Answer

$C=\left(4+\frac{9\sqrt2}{2},\frac{9\sqrt2}{2},2\right)$ or $C=\left(4-\frac{9\sqrt2}{2},-\frac{9\sqrt2}{2},2\right)$.

Vectors - Unit Vectors

Vectors - Unit Vectors

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