If vec{a} + 5vec{b} = vec{c} and vec{a} - 7ve | vedclass

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(A) Given equations are:$(1)$ $\vec{a} + 5\vec{b} = \vec{c}$$(2)$ $\vec{a} - 7\vec{b} = 2\vec{c}$Subtracting $(2)$ from $(1)$:$(\vec{a} + 5\vec{b}) -

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$\vec{a}$ and $\vec{c}$ are in the same direction,but $\vec{b}$ and $\vec{c}$ are in opposite directions.

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(A) Given equations are:$(1)$ $\vec{a} + 5\vec{b} = \vec{c}$$(2)$ $\vec{a} - 7\vec{b} = 2\vec{c}$Subtracting $(2)$ from $(1)$:$(\vec{a} + 5\vec{b}) - (\vec{a} - 7\vec{b}) = \vec{c} - 2\vec{c}$$12\vec{b} = -\vec{c}$$\vec{b} = -\frac{1}{12}\vec{c}$This implies $\vec{b}$ and $\vec{c}$ are in opposite directions.Now,substitute $\vec{b} = -\frac{1}{12}\vec{c}$ into $(1)$:$\vec{a} + 5(-\frac{1}{12}\vec{c}) = \vec{c}$$\vec{a} - \frac{5}{12}\vec{c} = \vec{c}$$\vec{a} = \vec{c} + \frac{5}{12}\vec{c} = \frac{17}{12}\vec{c}$Since $\frac{17}{12} > 0$,$\vec{a}$ and $\vec{c}$ are in the same direction.Thus,$\vec{a}$ and $\vec{c}$ are in the same direction,but $\vec{b}$ and $\vec{c}$ are in opposite directions.

If $\vec{a} + 5\vec{b} = \vec{c}$ and $\vec{a} - 7\vec{b} = 2\vec{c}$,then which of the following is true?

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