Chemistry, asked by awesomeraghav4829, 8 months ago

If a variable place in 3-0 space moves in such a way that the sum of its intercepts on the x and y-axis exceeds, the reciprocal of its intercept on the z-axis is by 2, then all such plane will pass through the point:
a) (1/2, 1/2, -1/2)
b) (1/2, 1/2, 1/2)
c) (1/2, -1/2, -1/2)
d) (1/2, -1/2, 1/2)

Answers

Answered by akanshaagrwal23
1

Explanation:

Let the equation of the variable plane be

a

x

+

b

y

+

c

z

=1 ...(1)

The intercepts on the coordinate axes are a,b,c.

The sum of reciprocals of intercepts in constant λ, therefore

a

1

+

b

1

+

c

1

=λ⇒

a

(1/λ)

+

b

(1/λ)

+

c

(1/λ)

∴(

λ

1

,

λ

1

,

λ

1

) lies on the plane (1)

Hence, the variable plane (1) always passes through the fixed point (

λ

1

,

λ

1

,

λ

1

ᵈᵉˢⁱ ᶜʰᵒʳᵃ

Answered by rockansh98
0

Answer:

Let the equation of the variable plane be

a

x

+

b

y

+

c

z

=1 ...(1)

The intercepts on the coordinate axes are a,b,c.

The sum of reciprocals of intercepts in constant λ, therefore

a

1

+

b

1

+

c

1

=λ⇒

a

(1/λ)

+

b

(1/λ)

+

c

(1/λ)

∴(

λ

1

,

λ

1

,

λ

1

) lies on the plane (1)

Hence, the variable plane (1) always passes through the fixed point (

λ

1

,

λ

1

,

λ

1

)

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