Condition for Concurrency of Three Lines
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A quadrilateral has the vertices at the points . Show that the mid points of the sides of this quadrilateral are the vertices of a parallelogram by using slope formula.
Three lines px+qy+r=0, qx+ry+p=0 and rx+py+q=0 are concurrent, if
- p+q+r=0
- p2+q2+r2=pr+rq
- p3+q3+r3=3pqr
- None of these
- 2√10
- 11√10
- 4√10
- 22√10
- PQ=RM
- QL=RM
- PL=SR
- PS=SM
Consider the lines given by
L1:x+3y−5=0
L2:3x−ky−1=0
L3:5x+2y−12=0
Match the Statements/Exp[ressions in Column I with the Statements/Expressions in Column II.
Column IColumn IIL1, L2, L3 are concurrent, ifk = -9One of L1, L2, L3 is parallel to at least one of the other two, ifk=65L1, L2, L3 form a triangle, ifk=56L1, L2, L3do not form a triangle, ifk = 5
(a) → (s), (b) → (p, q), (c) → (r), (d) → (p, q, s)
(a) → (p), (b) → (p, q, s), (c) → (r), (d) → (p, q)
(a) → (s), (b) → (p, q, s), (c) → (s, r), (d) → (p, q, s)
none of these
Three lines
L1 : x-y+6 = 0
L2 : 2x+y-3 = 0
L3 : x-2y+m = 0 are given. Which of the following can be the value of m if L1, L2 and L3 form a triangle.
10
11
12
13
The straight lines 2x+3y-12 = 0, x+y-5 = 0 and x-2y+1 = 0 are concurrent.
True
False
If 4a+5b+6c=0 then the set of lines ax+by+c=0 are concurrent at the point