If ABCD is a parallelogram and the position v | vedclass

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(B) In a parallelogram $ABCD$, the vectors representing opposite sides are equal, so $\overrightarrow{AB} = \overrightarrow{DC}$.Let the position vect

Vedclass · Accepted Answer

$7i + 9j + 11k$

Vedclass · Answer

(B) In a parallelogram $ABCD$, the vectors representing opposite sides are equal, so $\overrightarrow{AB} = \overrightarrow{DC}$.Let the position vector of $D$ be $\vec{d} = xi + yj + zk$.The position vectors are given as $\vec{a} = i + 3j + 5k$, $\vec{b} = i + j + k$, and $\vec{c} = 7i + 7j + 7k$.We know that $\overrightarrow{AB} = \vec{b} - \vec{a} = (1-1)i + (1-3)j + (1-5)k = 0i - 2j - 4k$.Similarly, $\overrightarrow{DC} = \vec{c} - \vec{d} = (7-x)i + (7-y)j + (7-z)k$.Equating $\overrightarrow{AB} = \overrightarrow{DC}$, we get:$0 = 7 - x \Rightarrow x = 7$$-2 = 7 - y \Rightarrow y = 9$$-4 = 7 - z \Rightarrow z = 11$Thus, the position vector of $D$ is $7i + 9j + 11k$.

If $ABCD$ is a parallelogram and the position vectors of $A, B, C$ are $i + 3j + 5k, i + j + k$ and $7i + 7j + 7k$, then the position vector of $D$ will be:

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