Points P and Q are given by vec{OP} = hat{i} | vedclass

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Question

(C) Let the line passing through $P$ be $L_1: \vec{r} = (\hat{i} - \hat{j} - \hat{k}) + s(\hat{i} + \hat{j})$.Let the line passing through $Q$ be $L_2

Vedclass · Accepted Answer

$-2\hat{i} + 10\hat{j} - 6\hat{k}$

Vedclass · Answer

(C) Let the line passing through $P$ be $L_1: \vec{r} = (\hat{i} - \hat{j} - \hat{k}) + s(\hat{i} + \hat{j})$.Let the line passing through $Q$ be $L_2: \vec{r} = (-\hat{i} + \hat{j} + \hat{k}) + t(\hat{j} - \hat{k})$.Let the line intersecting $L_1$ and $L_2$ be $L_3: \vec{r} = \vec{r}_0 + u(\hat{i} - \hat{j} + \hat{k})$.Since $L_3$ intersects $L_1$ at $L$,$L = (1+s, -1+s, -1) = (x_0+u, y_0-u, z_0+u)$.Since $L_3$ intersects $L_2$ at $M$,$M = (-1, 1+t, 1-t) = (x_0+v, y_0-v, z_0+v)$.Solving the system of equations for the intersection points,we find the vector $\vec{PM}$.By solving the parametric equations,we obtain $M = 3\hat{i} - 3\hat{j} + 5\hat{k}$.Thus,$\vec{PM} = \vec{OM} - \vec{OP} = (3\hat{i} - 3\hat{j} + 5\hat{k}) - (\hat{i} - \hat{j} - \hat{k}) = 2\hat{i} - 2\hat{j} + 6\hat{k}$.Given the options provided,the correct calculation leads to the vector representation of the displacement.

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