1. Tardigrade
  2. Question
  3. Mathematics
  4. The vectors a=x i-3 j-k and b=2 x i+x j-k include an acute angle and b and positive y-axis include an obtuse angle. Then values of x may be

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The vectors $a=x i-3 j-k$ and $b=2 x i+x j-k$ include an acute angle and $b$ and positive $y$-axis include an obtuse angle. Then values of $x$ may be

Vector Algebra

Solution:

According to the question
$a \cdot b>0$ and $b \cdot j<0 $
$\Rightarrow 2 x^{2}-3 x+1>0$ and $x<0$
$\Rightarrow (2 x-1)(x-1)>0$ and $x<0$
i.e., $\left(x<\frac{1}{2}\right.$ or $\left.x>1\right)$ and $x<0$
$ \Rightarrow x<0$