The position vectors of the points A, B, C ar | vedclass

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(C) Let the position vectors be $\vec{a} = 2i + j - k$,$\vec{b} = 3i - 2j + k$,and $\vec{c} = i + 4j - 3k$. Calculate the vectors $\vec{AB}$ and $\vec

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Are collinear

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(C) Let the position vectors be $\vec{a} = 2i + j - k$,$\vec{b} = 3i - 2j + k$,and $\vec{c} = i + 4j - 3k$. Calculate the vectors $\vec{AB}$ and $\vec{BC}$: $\vec{AB} = \vec{b} - \vec{a} = (3-2)i + (-2-1)j + (1-(-1))k = i - 3j + 2k$. $\vec{BC} = \vec{c} - \vec{b} = (1-3)i + (4-(-2))j + (-3-1)k = -2i + 6j - 4k$. Observe that $\vec{BC} = -2(i - 3j + 2k) = -2\vec{AB}$. Since $\vec{BC}$ is a scalar multiple of $\vec{AB}$,the vectors $\vec{AB}$ and $\vec{BC}$ are parallel. Because they share a common point $B$,the points $A, B$,and $C$ must be collinear.

The position vectors of the points $A, B, C$ are $(2i + j - k)$,$(3i - 2j + k)$,and $(i + 4j - 3k)$ respectively. These points

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