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Question

The equation of the palne passing through the line of intersection of the planes x+2y+3z−5=0 and 3x+2y−z+1=0 and cutting off equal intercepts on the OX and OZ axes is

A
2x+5y5z9=0
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B
5x2y5z+9=0
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C
5x+2y+5z9=0
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D
5x+5y2z+9=0
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Solution

The correct option is B 5x+2y+5z9=0

Any plane passing through the line of intersection of the given planes is

(x+2y+3z5)+λ(3x2yz+1)=0

(1+3λ)x+(22λ)y+(3λ)z+(5+λ)=0 ...(1)

Intercept on x-axis is 5λ1+3λ (Putting x=y=z=0)

Intercept on y-axis is 5λ3λ

Given: 5λ1+3λ=5λ3λλ=12

[λ=5 is not admissible as in taht case each intercept is zero]

Put λ=12 in (1), we get the equation of the required plane as 5x+2y+5z9=0


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