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Observe the following lists:
List-I(Plane) List-II (sum of the lengths of the intercepts on axes)
A) $3 x + 4 y - 5 z = 0$ 1) $- 77 / 30$
B) $2 x - 3 y + 5 z + 7 = 0$ 2) 13
C) $2 x + 3 y + 4 z - 12 = 0$ 3) 0
4) $217 / 30$
Match List-I to List-II:

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A B C

2 3 1

A B C

3 1 2

A B C

2 1 3

A B C

3 2 1

answer is A.

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Detailed Solution

intercept form of plane is $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$

$Sum = a + b + c$

For the plane A, it is passing through the origin, so the intercepts are equal to zero

Hence, the sum of the intercepts is zero

For the plane B, the sum of intercepts are $- \frac{7}{2} + \frac{7}{3} - \frac{7}{5} = \frac{- 105 + 70 - 42}{30} = - \frac{77}{30}$

For the plance C, the sum of intercepts is $\frac{12}{2} + \frac{12}{3} + \frac{12}{4} = 6 + 4 + 3 = 13$

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Observe the following lists:List-I(Plane) List-II (sum of the lengths of the intercepts on axes)A) 3x+4y-5z=0 1) -77/30B) 2x-3y+5z+7=0 2) 13C) 2x+3y+4z-12=0 3) 0 4) 217/30Match List-I to List-II:

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Observe the following lists:
List-I(Plane) List-II (sum of the lengths of the intercepts on axes)
A) $3 x + 4 y - 5 z = 0$ 1) $- 77 / 30$
B) $2 x - 3 y + 5 z + 7 = 0$ 2) 13
C) $2 x + 3 y + 4 z - 12 = 0$ 3) 0
4) $217 / 30$
Match List-I to List-II: