Vector Algebra Question 240
Question: If the position vectors of the point A, B, C be i, j, k respectively and P be a point such that $ \overrightarrow{AB}=\overrightarrow{CP}, $ then the position vector of P is
Options:
A) $ -\mathbf{i}+\mathbf{j}+\mathbf{k} $
B) $ -\mathbf{i}-\mathbf{j}+\mathbf{k} $
C) $ \mathbf{i}+\mathbf{j}-\mathbf{k} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- Let the position vector of P is $ x\mathbf{i}+y\mathbf{j}+z\mathbf{k}, $ then $ \overrightarrow{AB}=\overrightarrow{CP}\Rightarrow \mathbf{j}-\mathbf{i}=x\mathbf{i}+y\mathbf{j}+(z-1)\mathbf{k} $ By comparing the coefficients of $ \mathbf{i},\mathbf{j} $ and $ \mathbf{k}, $ we get $ x=-1, $ $ y=1,and,\text{z–1}=0\Rightarrow z=1 $ Hence required position vector is $ -\mathbf{i}+\mathbf{j}+\mathbf{k}. $
BETA
