BT STS

Q1. A and B are points with coordinates (2,1,3) and (4,-2,5) respectively. 2x+y-z=3 is the equation of a plane

(A) Line AB is parallel to the plane
(B) AB meets the plane at (0,4,1)
(c) The plane divides AB externally in the ration 1:2
(D) A and B are on the same side of the plane

MULTI ANSER

Q2. matrix
\vec{a} and \vec{b} are two unit vectors inclined at an angle \theta to each other. Then
\begin{matrix} \textup{Column 1} & \textup{Column 2}\\ (A)\; \left|\vec{a} +\vec{b}\right| < \sqrt{2} & (p)\; 2\pi /3<\theta <\pi \\ (B)\; \left|\vec{a} -\vec{b}\right| < \sqrt{2} & (q)\; \pi /3<\theta <\pi/2\\ (C)\; \left|\vec{a} +\vec{b}\right| < 1 & (r)\; \pi /2<\theta <\pi\\ (D)\; 1<\left|\vec{a} -\vec{b}\right| < \sqrt{2}& (s)\; 0<\theta <\pi/3\\ & (t)\; 0 <\theta <\pi /2 \end{matrix}