If the position vectors of the points A, B, C | vedclass

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(B) Given position vectors: $\vec{a} = 2i + 3j + 5k$,$\vec{b} = i + 2j + 3k$,$\vec{c} = -5i + 4j - 2k$,$\vec{d} = i + 10j + 10k$.Calculate vector $\ov

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$\overrightarrow{AB} \parallel \overrightarrow{CD}$

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(B) Given position vectors: $\vec{a} = 2i + 3j + 5k$,$\vec{b} = i + 2j + 3k$,$\vec{c} = -5i + 4j - 2k$,$\vec{d} = i + 10j + 10k$.Calculate vector $\overrightarrow{AB} = \vec{b} - \vec{a} = (1-2)i + (2-3)j + (3-5)k = -i - j - 2k$.Calculate vector $\overrightarrow{CD} = \vec{d} - \vec{c} = (1 - (-5))i + (10-4)j + (10 - (-2))k = 6i + 6j + 12k$.Observe that $\overrightarrow{CD} = -6(-i - j - 2k) = -6 \overrightarrow{AB}$.Since $\overrightarrow{CD}$ is a scalar multiple of $\overrightarrow{AB}$,the vectors are parallel. Thus,$\overrightarrow{AB} \parallel \overrightarrow{CD}$.

If the position vectors of the points $A, B, C, D$ are $2i + 3j + 5k, i + 2j + 3k, -5i + 4j - 2k$ and $i + 10j + 10k$ respectively,then:

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