Vector Algebra Question 236
Question: If ABCD is a parallelogram and the position vectors of A, B, C are $ \mathbf{i}+3\mathbf{j}+5\mathbf{k},\mathbf{i}+\mathbf{j}+\mathbf{k} $ and $ 7\mathbf{i}+7\mathbf{j}+7\mathbf{k}, $ then the position vector of D will be
Options:
A) $ 7\mathbf{i}+5\mathbf{j}+3\mathbf{k} $
B) $ 7\mathbf{i}+9\mathbf{j}+11\mathbf{k} $
C) $ 9\mathbf{i}+11\mathbf{j}+13\mathbf{k} $
D) $ 8\mathbf{i}+8\mathbf{j}+8\mathbf{k} $
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Answer:
Correct Answer: B
Solution:
- Let position vector of D is $ x\mathbf{i}+y\mathbf{j}+z\mathbf{k}, $ then $ \overrightarrow{AB}=\overrightarrow{DC} $
$ \Rightarrow -2\mathbf{j}-4\mathbf{k}=(7-x)\mathbf{i}+(7-y)\mathbf{j}+(7-z)\mathbf{k} $
$ \Rightarrow x=7,y=9,z=11. $ Hence position vector of $ D $ will be $ 7\mathbf{i}+9\mathbf{j}+11,\mathbf{k} $ .
BETA
