Phytochrome is a

Let $P(a\sec \theta, b\tan \theta)$ and $Q(a\sec \varphi, b\tan \varphi)$,where $\theta + \varphi = \frac{\pi}{2}$,be two points on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If $(h, k)$ is the point of intersection of the normals at $P$ and $Q$,then $k$ is equal to

The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$ and $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)$ is:

Cerium $(Z = 58)$ is an important member of the lanthanoids. Which of the following statements is $NOT$ correct for Cerium?

The line passing through $\left(-1, \frac{\pi}{2}\right)$ and perpendicular to $\sqrt{3} \sin \theta + 2 \cos \theta = \frac{4}{r}$ is :

If $a = 2i + j - k, b = i + 2j + k$ and $c = i - j + 2k,$ then $a \cdot (b \times c) = $