Vector Algebra Question 386
Question: If three points A, B and C have position vectors $ (1,,x,,3),(3,,4,,7) $ and $ ap+bq+cr=1 $ respectively and if they are collinear, then $ (x,,y)= $
[EAMCET 2002]
Options:
A) (2, ? 3)
B) (? 2, 3)
C) (2, 3)
D) (? 2, ? 3)
Show Answer
Answer:
Correct Answer: A
Solution:
- If A, B, C are collinear. Then $ \overrightarrow{AB}=\lambda ,\overrightarrow{BC} $
Þ $ 2\mathbf{i}+(4-x)\mathbf{j}+4\mathbf{k}=\lambda ,[(y-3)\mathbf{i}-6\mathbf{j}-12\mathbf{k}] $
$ \Rightarrow ,2=(y-3)\lambda $ …..(i) and $ 4-x=-6,\lambda $ …..(ii) Þ $ 4=-12,\lambda ,\Rightarrow \lambda =\frac{-1}{3} $ By (i), $ y=-3 $ and by (ii), $ x=2 $ ;
$ \therefore ,(x,,y)=(2,,-3). $
BETA
