Vector Algebra Question 29
Question: The value of k for which the vectors $ \mathbf{a}=\mathbf{i}-\mathbf{j} $ and $ \mathbf{b}=-2,\mathbf{i}+k,\mathbf{j} $ are collinear is
[Pb. CET 2004]
Options:
A) 2
B) $ \frac{1}{2} $
C) $ \frac{1}{3} $
D) 3
Show Answer
Answer:
Correct Answer: A
Solution:
- Since $ \mathbf{a} $ and $ \mathbf{b} $ are collinear, we have $ \mathbf{a}=m\mathbf{b} $ for some scalar m.
Þ $ \mathbf{i}-\mathbf{j}=m(-2\mathbf{i}+k\mathbf{j}) $
Þ $ \mathbf{i}-\mathbf{j}=-2m\mathbf{i}+km\mathbf{j} $
Þ $ -2m=1,,km=-1 $ \ $ m=-\frac{1}{2}, $ So $ k=2 $ .
BETA
