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Ask QuestionPosted by Suman Sharma 5 years, 8 months ago
- 4 answers
Yogita Ingle 5 years, 8 months ago
Since x-coordinate of every point in yz-plane is zero. Let P (0, y, z) be a point on the yz-plane such that PA = PB = PC.
Now PA = PB
(0 – 2)2 + (y – 0)2 + (z – 3)2 = (0 – 0)2 + (y – 3)2 + (z – 2)2
i.e. z – 3y = 0
and PB = PC
⇒ y2 + 9 – 6y + z2 + 4 – 4z = y2 + z2 + 1 – 2z ,
i.e. 3y + z = 6 Simplifying the two equating, we get y = 1, z = 3
Here, the coordinate of the point P are (0, 1, 3).
Posted by Suman Sharma 5 years, 8 months ago
- 2 answers
Yogita Ingle 5 years, 8 months ago
let the point p be (h, k)
Now 2PA,=3PB
PA=√[h^2+k^2]
pb=√[h-4]^2+[k+3]^2
given 2PA=3PB
SQ. both sides
4PAsq. =9PBsq
4(h^2+k^2)=9[(h-4)^2+(k+3)^2]
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Yogita Ingle 5 years, 9 months ago
The odd integers from 1 to 2001 are 1, 3, 5, …1999, 2001.
This sequence forms an A.P.
Here, first term, a = 1
Common difference, d = 2
Here,<nobr>
a+(n−1)d=2001
=>1+(n−1)(2)=2001
=>2n−2=2000
=>n=1001
Sn= n2[2a+(n−1)d]
∴Sn= 10012[2×1+(1001−1)×2]
= 10012 [2+1000 × 2]
=10012×2002
=1001×1001
=1002001</nobr>
Thus, the sum of odd numbers from 1 to 2001 is 1002001.
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Suman Sharma 5 years, 8 months ago
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