Practicing Success
The values of x for which the angle between the vectors $\vec a = x\hat i- 3\hat j-\hat k$ and $\vec b = 2x\hat i + x\hat j-\hat k$ is acute, and the angle between the vector $\vec b$ and the axis of ordinates is obtuse, are |
$\frac{1}{2},2$ $-2,3$ all x < 0 all x > 0 |
all x < 0 |
Since the angle between the vectors $\vec a$ and $\vec b$ is acute and the angle between $\vec b$ and y-axis is obtuse. Therefore, $\vec a.\vec b>0$ and $\vec b.\hat j<0$ $⇒2x^2-3x+1>0$ and $x <0$ $⇒(2x-1) (x-1) > 0$ and $x <0$ $⇒(x <1/2\, or\, x > 1)$ and $x <0⇒ x <0$ |