\( z_{1}, z_{2}, z_{3} \) represents distinct points \( A, B, C \) in Argand
Plane.
\begin{tabul....
\( z_{1}, z_{2}, z_{3} \) represents distinct points \( A, B, C \) in Argand
Plane.
\begin{tabular}{|c|c|c|c|c|c|}
\hline \multicolumn{2}{|r|}{ Column-I } & \multicolumn{2}{|c|}{ Column-II } & & \\
\hline (A) & \( 2 z_{1} z_{3}=z_{1} z_{2}+z_{2} z_{3} \) & (P) & \begin{tabular}{l}
\( A, B, C \) are \\
collinear
\end{tabular} & & \\
\hline (B) & \begin{tabular}{l}
\( \left|z_{3}-z_{1}\right|^{2}+\left|z_{3}-z_{2}\right|^{2} \) \\
\( =\left|z_{1}-z_{2}\right|^{2} \)
\end{tabular} & (Q) & \begin{tabular}{l}
\( A, B, C \) lie \\
on circle \\
whose \\
diameter \\
is \( A B \)
\end{tabular} & & \\
\hline (C) & \begin{tabular}{l}
\( \lambda_{1}, \lambda_{2}, \lambda_{3} \in \) real, \( \lambda_{1} z_{1}+ \) \\
\( \lambda_{2} z_{2}+\lambda_{3} z_{3}=0, \lambda_{1}+\lambda_{2}+ \) \\
\( \lambda_{3}=0 \)
\end{tabular} & (R) & \begin{tabular}{l}
\( A, B, C \) lie \\
in circle \\
which \\
passes \\
through \\
\( \mathrm{O}(0,0) \)
\end{tabular} & & \\
\hline (D) & \begin{tabular}{l}
\( \frac{1}{z_{1}-z_{2}}+\frac{1}{z_{2}-z_{3}} \) \\
\( +\frac{1}{z_{3}-z_{1}}=0 \)
\end{tabular} & (S) & \begin{tabular}{l}
\( A, \quad B, \quad C \) \\
make \\
equilateral \\
triangle
\end{tabular} & \begin{tabular}{l}
\( (1) \) \\
\( (2) \) \\
\( (3) \) \\
\( (4) \)
\end{tabular} & \begin{tabular}{l}
A-P; B-Q; C-R; D-S \\
A-P; B-R; C-S; D-S \\
A-R; B-Q; C-P; D-S \\
A-P;B-R; C-S; D-Q
\end{tabular} \\
\hline
\end{tabular}
π²PW App Link - https://bit.ly/YTAI_PWAP
πPW Website - https://www.pw.live
Other Videos By PW Solutions
| 2024-01-21 | If [.] denotes the greatest integer function, then
\( \lim _{x \rightarrow 0} \frac{\tan \left(\.... |
| 2024-01-21 | \( \lim _{x \rightarrow \infty}\left\{\left(\frac{x}{x+1}\right)^{a} a+\sin \frac{1}{x}\right\}^.... |
| 2024-01-21 | The largest value of the non-negative integer \( a \) for
which \( \lim _{\alpha \rightarrow 1}\.... |
| 2024-01-21 | The value of
\( \lim _{x \rightarrow 0}\left\{\frac{1}{1 \sin ^{2} x}+2^{\frac{1}{\sin ^{2} x}}+.... |
| 2024-01-21 | Let \( f: R \rightarrow R \) be such that \( f(1)=3 \) and \( f^{\prime}(1)=6 \).
Then, \( \lim .... |
| 2024-01-21 | Let \( x^{2}+3 y^{2}=3 \) be the equation of an ellipse in the
\( x y \)-plane. If \( A(-\sqrt{3.... |
| 2024-01-21 | If the Coordinates of the point which trisect the line
segment joining the point \( P(4,2,-6) \).... |
| 2024-01-21 | Match the pair of points in List-I with their direction cosines in List -II.
\begin{tabular}{|l|.... |
| 2024-01-21 | Match the points in List-I with their octants in List-II
\begin{tabular}{|l|l|l|l|}
\hline & Lis.... |
| 2024-01-21 | If the Coordinates of the point which trisect the line
segment joining the point \( P(4,2,-6) \).... |
| 2024-01-21 | \( z_{1}, z_{2}, z_{3} \) represents distinct points \( A, B, C \) in Argand
Plane.
\begin{tabul.... |
| 2024-01-21 | Consider two points \( P(-2,3,5) \) and \( Q(1,-4,3) \) then
The point where \( P Q \) meets \( .... |
| 2024-01-21 | Consider two points \( P(-2,3,5) \) and \( Q(1,-4,3) \) then
The point where \( P Q \) meets \( .... |
| 2024-01-21 | Distance of point \( P \) from origin is 7 units from \( x \)-axis
is \( \sqrt{13} \) units and .... |
| 2024-01-21 | If the centroid of triangle whose vertices are \( (a, 1,3) \),
\( (-2, b,-5) \) and \( (4,7, c) .... |
| 2024-01-21 | \( M \) is the foot of the perpendicular drawn from a point
\( P(9,-2,6) \) on the \( x y \)-pla.... |
| 2024-01-21 | The ratio in which the line segment joining the point
\( (2,4,7) \) and \( (-8,6,1) \) is divide.... |
| 2024-01-21 | What does the equation \( x^{2}-x-6=0 \) represent in \( 3 \mathrm{D} \)
coordinate system?.... |
| 2024-01-21 | The points \( (-1,2,1),(1,-2,5),(4,-7,8) \) and
\( (2,-3,4) \) are the vertices of a.... |
| 2024-01-21 | The equation of plane passing through the point
\( (5,7,-2) \) and which is parallel to \( y z \.... |
| 2024-01-21 | The coordinates of the point which divides the line
segment joining the points \( (-4,2,3) \) an.... |
0