Vector Algebra Question 362
Question: The value of x for which the angle between the vectors $ \mathbf{a}=-,3\mathbf{i}+x\mathbf{j}+\mathbf{k} $ and $ \mathbf{b}=x\mathbf{i}+2x\mathbf{j}+\mathbf{k} $ is acute and the angle between b and x-axis lies between $ \pi /2 $ and $ \pi $ satisfy
[Kurukshetra CEE 1996]
Options:
A) $ x>0 $
B) $ x<0 $
C) $ x>1 $ only
D) $ x<-1 $ only
Show Answer
Answer:
Correct Answer: B
Solution:
- For acute angle $ \mathbf{a},.,\mathbf{b}>0 $ i.e., $ -3x+2x^{2}+1>0\Rightarrow (x-1)(2x-1)>0 $ For obtuse angle between $ \mathbf{b} $ and x-axis $ \mathbf{b},.,\mathbf{i}<0 $
Þ $ x<0 $ .
BETA
