Consider the following linear equations:
$ax+by+cz=0$,$bx+cy+az=0$,$cx+ay+bz=0$
Match the conditions/expressions in Column $I$ with statements in Column $II$:
Column $I$ Column $II$ $(A)$ $a+b+c \neq 0$ and $a^2+b^2+c^2=ab+bc+ca$ $(p)$ The equations represent planes meeting only at a single point. $(B)$ $a+b+c=0$ and $a^2+b^2+c^2 \neq ab+bc+ca$ $(q)$ The equations represent the line $x=y=z$. $(C)$ $a+b+c \neq 0$ and $a^2+b^2+c^2 \neq ab+bc+ca$ $(r)$ The equations represent identical planes. $(D)$ $a+b+c=0$ and $a^2+b^2+c^2=ab+bc+ca$ $(s)$ The equations represent the whole of the three-dimensional space.
$ax+by+cz=0$,$bx+cy+az=0$,$cx+ay+bz=0$
Match the conditions/expressions in Column $I$ with statements in Column $II$:
| Column $I$ | Column $II$ |
| $(A)$ $a+b+c \neq 0$ and $a^2+b^2+c^2=ab+bc+ca$ | $(p)$ The equations represent planes meeting only at a single point. |
| $(B)$ $a+b+c=0$ and $a^2+b^2+c^2 \neq ab+bc+ca$ | $(q)$ The equations represent the line $x=y=z$. |
| $(C)$ $a+b+c \neq 0$ and $a^2+b^2+c^2 \neq ab+bc+ca$ | $(r)$ The equations represent identical planes. |
| $(D)$ $a+b+c=0$ and $a^2+b^2+c^2=ab+bc+ca$ | $(s)$ The equations represent the whole of the three-dimensional space. |
- A$A-q, B-r, C-s, D-p$
- B$A-s, B-r, C-q, D-p$
- C$A-p, B-q, C-s, D-r$
- D$A-r, B-q, C-p, D-s$
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