The position vectors of points A, B, C and D | vedclass

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(C) The displacement vector $\overrightarrow{AB}$ is given by $\overrightarrow{B} - \overrightarrow{A} = (4-3)\hat{i} + (5-4)\hat{j} + (6-5)\hat{k} =

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Antiparallel

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(C) The displacement vector $\overrightarrow{AB}$ is given by $\overrightarrow{B} - \overrightarrow{A} = (4-3)\hat{i} + (5-4)\hat{j} + (6-5)\hat{k} = \hat{i} + \hat{j} + \hat{k}$.The displacement vector $\overrightarrow{CD}$ is given by $\overrightarrow{D} - \overrightarrow{C} = (4-7)\hat{i} + (6-9)\hat{j} + (0-3)\hat{k} = -3\hat{i} - 3\hat{j} - 3\hat{k}$.We can rewrite $\overrightarrow{CD}$ as $\overrightarrow{CD} = -3(\hat{i} + \hat{j} + \hat{k}) = -3\overrightarrow{AB}$.Since $\overrightarrow{CD} = k\overrightarrow{AB}$ where $k = -3$ (a negative constant),the vectors are parallel but point in opposite directions,which means they are antiparallel.

The position vectors of points $A, B, C$ and $D$ are $\vec A = 3\hat i + 4\hat j + 5\hat k, \vec B = 4\hat i + 5\hat j + 6\hat k, \vec C = 7\hat i + 9\hat j + 3\hat k$ and $\vec D = 4\hat i + 6\hat j$. Then the displacement vectors $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are:

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