1
Question
z1, z2, z3 are vertices of a triangle
Match the following functions given in Column-I with the ranges given in Column-ll
Column-I Column-II
1. z12+z22+z32=z2z3+z3z1+z1z2 (p) right angled
2. Re(z3−z1z3−z2)=0 (q) obtuse angled
3. Re(z3−z1z3−z2)<0 (r) Isosceles and right angled
4. z3−z1z3−z2=i (s) equilateral
Match the following functions given in Column-I with the ranges given in Column-ll
Column-I Column-II
1. z12+z22+z32=z2z3+z3z1+z1z2 (p) right angled
2. Re(z3−z1z3−z2)=0 (q) obtuse angled
3. Re(z3−z1z3−z2)<0 (r) Isosceles and right angled
4. z3−z1z3−z2=i (s) equilateral
Open in App
Solution
The correct options are
A 2→p
B 3→q
C 1→s
D 4→r
We know that
z21+z22+z23=z1z2+z2z3+z3z1 holds for equilateral triangle.
Now
Let ABCD be a polygon,
A=z1
B=z2
C=z3
D=z4
Now Re(z3−z1z3−z2)=0 indicates that it is purely real. That is its argument is π2
Hence right angled.
Now
consider Re(z3−z1z3−z2)<0
That is cosθ<0
This is possible if θ is obtuse and does not lie in the fourth quadrant.
If
z3−z1z3−z2=i
Then Re(z3−z1z3−z2)=0 indicates that it is purely real. That is its argument is π2
Hence right angled, and
|z3−z1|=|z3−z2|
Hence isosceles.
All options are correct.
A 2→p
B 3→q
C 1→s
D 4→r
We know that
z21+z22+z23=z1z2+z2z3+z3z1 holds for equilateral triangle.
Now
Let ABCD be a polygon,
A=z1
B=z2
C=z3
D=z4
Now Re(z3−z1z3−z2)=0 indicates that it is purely real. That is its argument is π2
Hence right angled.
Now
consider Re(z3−z1z3−z2)<0
That is cosθ<0
This is possible if θ is obtuse and does not lie in the fourth quadrant.
If
z3−z1z3−z2=i
Then Re(z3−z1z3−z2)=0 indicates that it is purely real. That is its argument is π2
Hence right angled, and
|z3−z1|=|z3−z2|
Hence isosceles.
All options are correct.
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
