Vector Algebra Question 280
Question: If the position vectors of the points A, B, C be $ \mathbf{i}+\mathbf{j},,\mathbf{i}-\mathbf{j} $ and $ a\mathbf{i}+b,\mathbf{j}+c,\mathbf{k} $ respectively, then the points A, B, C are collinear if
Options:
A) $ a=b=c=1 $
B) $ a=1,b $ and $ c $ are arbitrary scalars
C) $ a=b=c=0 $
D) $ c=0,a=1 $ and b is arbitrary scalars
Show Answer
Answer:
Correct Answer: D
Solution:
- Here $ \overrightarrow{AB}=-2\mathbf{j}, $ $ \overrightarrow{BC}=(a-1)\mathbf{i}+(b+1)\mathbf{j}+c\mathbf{k} $ The points are collinear, then $ \overrightarrow{AB}=k,(\overrightarrow{BC}) $ $ -2\mathbf{j}=k{(a-1)\mathbf{i}+(b+1),\mathbf{j}+c\mathbf{k}} $ On comparing, $ k,(a-1)=0 $ , $ k(b+1)=-2, $ $ kc=0 $ . Hence $ c=0, $ $ a=1 $ and $ b $ is arbitrary scalar.
BETA
