Position vectors of the points A, B and C as shown in the figure below are a, $\vec{b}$ and $\vec{c}$ respectively. If $\vec{AC}=\frac{5}{4}\vec{AB}$ , express $\vec{c}$ in terms of $\vec{a}$ and $\vec{b}$ . OR Check whether the lines given by equations $x=2\lambda+2$, $y=7\lambda+1$, $z=-3\lambda-3$ and $x=-\mu-2,$ $y=2\mu+8,$ $z=4\mu+5$ are perpendicular to each other or not.

If the direction cosines of a line are $(\frac{1}{a}, \frac{1}{a}, \frac{1}{a})$ then:

If the direction cosines of a line are \(\sqrt{3}k, \sqrt{3}k\), \(\sqrt{3}k,\) then the value of k is:

The angle which the line \(\frac{x}{1}=\frac{y}{-1}=\frac{z}{0}\) makes with the positive direction of Y-axis is:

25. (a) Find the vector equation of the line passing through the point $(2, 1, 3)$ and perpendicular to both the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3} ; \frac{x}{-3}=\frac{y}{2}=\frac{z}{5}$