1 Answer

Bozzle · Answer 1 · 2024-09-13T21:14:26+0000

Let's first understand what's relative here, it refers to Point of reference , the point, in respect to which other's position are to be considered, which here is O, the Origin with coordinates (0,0) as we are talking about two-dimensional reference frame. What position vector means? Say, we have the point of Reference X, and we've the position vector of Y with respect to X, then it can be written as
${\overrightarrow{XY}}$ . Now, using this simple rule we can have,

${\overrightarrow{OA}=-2\hat{i}+7\hat{j}}$
${\overrightarrow{OB}=2\hat{i}-\hat{j}}$
${\overrightarrow{OC}=6\hat{i}+\lambda \hat{j}}$

Now, let's calculate
${\overrightarrow{AC}}$ firstly;

${:\implies \overrightarrow{AC}=\overrightarrow{OC}-\overrightarrow{OA}}$

${:\implies \overrightarrow{AC}=8\hat{i}+(\lambda -7)\hat{j}}$

Now, here
{AC} just means the the magnitude of the vector [tex{\overrightarow{AC}}[/tex], and we're aware that magnitude of a vector
${\overrightarrow{X}=x\hat{i}+y\hat{j}}$ is given by,
${X=\sqrt{x^(2)+y^(2)}}$ , so according to question;