If P, Q, R and S are the points with position | vedclass

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(A) Given position vectors are: $\vec{OP} = \hat{i} + \hat{j} - \hat{k}$ $\vec{OQ} = 2\hat{i} - \hat{j} + 3\hat{k}$ $\vec{OR} = 2\hat{i} - 3\hat{k}$ $

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(A) Given position vectors are: $\vec{OP} = \hat{i} + \hat{j} - \hat{k}$ $\vec{OQ} = 2\hat{i} - \hat{j} + 3\hat{k}$ $\vec{OR} = 2\hat{i} - 3\hat{k}$ $\vec{OS} = 3\hat{i} - 2\hat{j} + \hat{k}$ Now, calculate the vectors $\vec{PQ}$ and $\vec{RS}$: $\vec{PQ} = \vec{OQ} - \vec{OP} = (2\hat{i} - \hat{j} + 3\hat{k}) - (\hat{i} + \hat{j} - \hat{k}) = \hat{i} - 2\hat{j} + 4\hat{k}$ $\vec{RS} = \vec{OS} - \vec{OR} = (3\hat{i} - 2\hat{j} + \hat{k}) - (2\hat{i} - 3\hat{k}) = \hat{i} - 2\hat{j} + 4\hat{k}$ Since $\vec{PQ} = \vec{RS}$, the vectors are parallel. The angle between two parallel vectors is $0$.

If $P, Q, R$ and $S$ are the points with position vectors $\hat{i}+\hat{j}-\hat{k}, 2 \hat{i}-\hat{j}+3 \hat{k}, 2 \hat{i}-3 \hat{k}$ and $3 \hat{i}-2 \hat{j}+\hat{k}$ respectively, then the angle between $PQ$ and $RS$ is

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