The two planes ax + by + cz + d = 0 and ax + by + cz + d1 = 0, where d

1.	The two planes ax + by + cz + d = 0 and ax + by + cz + d1 = 0, where d ≠ d1, have1. one point only in common2. three points in common3. infinite points in common4. no points in common
Answer» Correct Answer - Option 4 : no points in common Concept: If planes are parallel, no point in common. If planes are perpendicular, only one point in common. If plane coincides then infinite points in common Calculations: Given, the equation of two planes ax + by + cz + d = 0 and ax + by + cz + d1 = 0, where d ≠ d1. Taking the ratio of direction ratios of the plane, we have ⇒ \(\rm \dfrac a a = \dfrac b b = \dfrac c c \) ⇒ 1 = 1= 1. ⇒The ratio of direction ratios of the plane ax + by + cz + d = 0 and ax + by + cz + d1 = 0 is same ⇒ The plane ax + by + cz + d = 0 and ax + by + cz + d1 = 0 are parallel. Hence, The two planes ax + by + cz + d = 0 and ax + by + cz + d1 = 0, where d ≠ d1, have no points in common.

The two planes ax + by + cz + d = 0 and ax + by + cz + d1 = 0, where d ≠ d1, have1. one point only in common2. three points in common3. infinite points in common4. no points in common

Answer» Correct Answer - Option 4 : no points in common

Concept:

If planes are parallel, no point in common.

If planes are perpendicular, only one point in common.

If plane coincides then infinite points in common

Calculations:

Given, the equation of two planes ax + by + cz + d = 0 and ax + by + cz + d1 = 0, where d ≠ d1.

Taking the ratio of direction ratios of the plane, we have

⇒ \(\rm \dfrac a a = \dfrac b b = \dfrac c c \)

⇒ 1 = 1= 1.

⇒The ratio of direction ratios of the plane ax + by + cz + d = 0 and ax + by + cz + d1 = 0 is same

⇒ The plane ax + by + cz + d = 0 and ax + by + cz + d1 = 0 are parallel.

Hence, The two planes ax + by + cz + d = 0 and ax + by + cz + d1 = 0, where d ≠ d1, have no points in common.

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