Match the conditions/expressions in Column $$I$$ with statements in Column $$II$$ and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the $$ORS.$$
$$\,\,\,$$ Column $$I$$
(A)$$\,\,a + b + c \ne 0$$ and $${a^2} + {b^2} + {c^2} = ab + bc + ca$$
(B)$$\,\,$$ $$a + b + c = 0$$ and $${a^2} + {b^2} + {c^2} \ne ab + bc + ca$$
(C)$$\,\,a + b + c \ne 0$$ and $${a^2} + {b^2} + {c^2} \ne ab + bc + ca$$
(D)$$\,\,$$ $$a + b + c = 0$$ and $${a^2} + {b^2} + {c^2} = ab + bc + ca$$
$$\,\,\,$$ Column $$II$$
(p)$$\,\,\,$$ the equations represents planes meeting only at asingle point
(q)$$\,\,\,$$ the equations represents the line $$x=y=z.$$
(r)$$\,\,\,$$ the equations represent identical planes.
(s) $$\,\,\,$$ the equations represents the whole of the three dimensional space.
STATEMENT-1: The parametric equations of the line of intersection of the given planes are $$x=3+14t,y=1+2t,z=15t.$$ because
STATEMENT-2: The vector $${14\widehat i + 2\widehat j + 15\widehat k}$$ is parallel to the line of intersection of given planes.
STATEMENT-1: $$\overrightarrow {PQ} \times \left( {\overrightarrow {RS} + \overrightarrow {ST} } \right) \ne \overrightarrow 0 .$$ because
STATEMENT-2: $$\overrightarrow {PQ} \times \overrightarrow {RS} = \overrightarrow 0 $$ and $$\overrightarrow {PQ} \times \overrightarrow {ST} \ne \overrightarrow 0 \,\,.$$
Column I
(A) GMeMs ,
G $$ \to $$ universal gravitational constant, Me $$ \to $$ mass of the earth,
Ms $$ \to $$ mass of the Sun
(B) $${{3RT} \over M}$$,
R $$ \to $$ universal gas constant, T $$ \to $$ absolute temperature,
M $$ \to $$ molar mass
(C) $${{{F^2}} \over {{q^2}{B^2}}}$$ ,
F $$ \to $$ force, q $$ \to $$ charge, B $$ \to $$ magnetic field
(D) $${{G{M_e}} \over {{R_e}}}$$,
G $$ \to $$ universal gravitational constant,
Me $$ \to $$ mass of the earth, Re $$ \to $$ radius of the earth
Column II
(p) (volt) (coulomb) (metre)
(q) (kilogram) (metre)3 (second)−2
(r) (meter)2(second)−2
(s) (farad) (volt)2 (kg)−1