Originally Posted by

**bigmansouf** I have attached my question

here is my attempt:

I have attached my question

Here's my attempt :

$\displaystyle \overrightarrow{OA}= 2\mathbf{i}+3\mathbf{j} $

$\displaystyle \overrightarrow{OB}= 3\mathbf{i} - \mathbf{j} + k(\mathbf{i}+2\mathbf{j}) $

$\displaystyle \overrightarrow{OC}= 4\mathbf{i} + 13\mathbf{j} + k(\mathbf{4i}-\mathbf{j})$

$\displaystyle \overrightarrow{OB}= (3+k)\mathbf{i} + (2k-1)\mathbf{j} $

$\displaystyle \overrightarrow{OC}= (4+4k)\mathbf{i}+(13-k)\mathbf{j} $

$\displaystyle (4+4k)\mathbf{i}+(13-k)\mathbf{j} = (3+k)\mathbf{i} + (2k-1)\mathbf{j} $ since OB is parallel to OC