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Properties of Distance

1.find the eq...

Question

1.find the equation of the line passing through the point(2,3) and making intercept of lengh 2 units between the lines Y+2X=3 and Y+2X =5. 2.Let (x,y,z) be points with integer co-ordinates satisfying the system of homogeneous equations 3x-y-z=0,-3x+z=0,-3x+ 2y +z=0.The no of such points for which x2(square) + y2(square)+z2(square) is less than or equal to100.

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(x, y, z)

3 x - y - z = 0 . . . (i)

- 3 x + z = 0 . . . (i i)

- 3 x + 2 y + z = 0 . . . (i i i)

x^{2} + y^{2} + z^{2} \leq 100

(x, y, z)

3 x - y - z = 0

- 3 x + z = 0

- 3 x + 2 y + z = 0

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(1, - 2, 3)

x - y + 2 z - 5 = 0

3 x + y + z - 6 = 0

5 x + 2 z - 8 = 0

2 x - y + z - 3 = 0

3 x + y + z = 5

2 x - y - 5 z - 3 = 0

3 x + y + z = 5

x - 1 = y + 1 = z - 1

(1, 1, 1)

2 x + 3 y - 4 z = 1

3 x - y + z + 2 = 0

4

x

2 x + 3 y - 4 z - 1 + λ (3 x - y + z + 2) = 0

λ

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