Jee Advanced
Straight Lines And Pair Of Straight Lines
IIT-JEE 2007 Paper 1 Offline
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.
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
.tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;}
.tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top}
.tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top}
.tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top}
| Column I | Column II | ||
|---|---|---|---|
| (A) | \(a + b + c \ne 0\) 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 \({a^2} + {b^2} + {c^2} \ne ab + bc + ca\) | (Q) | the equations represent the line \(x=y=z\). |
| (C) | \(a + b + c \ne 0\) and \({a^2} + {b^2} + {c^2} \ne ab + bc + ca\) | (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. |