In the figure,a vector x satisfies the equati | vedclass

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(D) From the triangle law of vector addition in $	riangle ADC$,we have $\vec{AD} + \vec{DC} = \vec{AC}$. Given $\vec{AD} = b$ and $\vec{DC} = v$,we h

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$a + b + c$

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(D) From the triangle law of vector addition in $	riangle ADC$,we have $\vec{AD} + \vec{DC} = \vec{AC}$. Given $\vec{AD} = b$ and $\vec{DC} = v$,we have $\vec{AC} = b + v$. However,looking at the triangle $	riangle ADC$,the vector $v$ is directed from $C$ to $D$,so $\vec{DC} = -v$. Thus,$\vec{AC} = b - v$. From the triangle law in $	riangle ABD$,$\vec{AB} + \vec{BD} = \vec{AD}$. Given $\vec{AB} = a$ and $\vec{BD} = w$,we have $a + w = b$,so $w = b - a$. Given $x - w = v$,we have $x = v + w$. Substituting the vectors from the figure: In $	riangle ADC$,$\vec{AC} = \vec{AD} + \vec{DC}$. If we define the vectors based on the directions shown: $w = \vec{BD}$,$v = \vec{CD}$. From $	riangle ABD$,$\vec{AD} = \vec{AB} + \vec{BD} = a + w$. From $	riangle ADC$,$\vec{AC} = \vec{AD} + \vec{DC} = (a + w) + v$. Given the equation $x = v + w$,and observing the geometry,the correct vector sum is $x = a + b + c$.

In the figure,a vector $x$ satisfies the equation $x - w = v$. Then $x =$

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