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

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(B) The displacement vector $\overrightarrow{AB}$ is calculated as: $\overrightarrow{AB} = \vec{B} - \vec{A} = (4\hat{i} + 5\hat{j} + 6\hat{k}) - (3\h

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Antiparallel

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(B) The displacement vector $\overrightarrow{AB}$ is calculated as: $\overrightarrow{AB} = \vec{B} - \vec{A} = (4\hat{i} + 5\hat{j} + 6\hat{k}) - (3\hat{i} + 4\hat{j} + 5\hat{k}) = \hat{i} + \hat{j} + \hat{k}$.The displacement vector $\overrightarrow{CD}$ is calculated as: $\overrightarrow{CD} = \vec{D} - \vec{C} = (4\hat{i} + 6\hat{j}) - (7\hat{i} + 9\hat{j} + 3\hat{k}) = -3\hat{i} - 3\hat{j} - 3\hat{k}$.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 scalar),the vectors $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are antiparallel.

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

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