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Yogita Ingle 1 week ago
As the name represents, the finite set is a set having finite or countable number of elements.
Example set of all English alphabets.
A set which is not a finite set is called an Infinite Set. Or if you cannot count the number of elements of a particular set then it is said to be an infinite set.
N is a set of all natural numbers starting from zero. Its number of elements is not countable so we use the three dots to represent itsinfinity.
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Two sets A and B can be equal only if each element of set A is also the element of the set B. Also if two sets are the subsets of each other, they are said to be equal. This is represented by:
A = B
To be equivalent, the sets should have the same cardinality. This means that there should be one to one correspondence between elements of both the sets. Here, one to one correspondence means that for each element in the set A, there exists an element in the set B till the sets get exhausted.
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Yogita Ingle 2 weeks 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 2 weeks ago
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Yogita Ingle 2 weeks 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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