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The plane passing through the point (−2, −2, 2) and containing the line joining the points

(1, 1, 1) and (1, −1, 2) makes intercepts on the coordinates axes then sum of the lengths of intercepts is

  • a)
    3

  • b)
    4

  • c)
    6

  • d)
    12

Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The plane passing through the point (−2, −2, 2) and contai...
Equation of any plane passing through (−2, −2, 2) is 
a(x + 2) + b(y + 2) + c(z – 2) = 0
Since it contains the line joining the points (1, 1, 1) and (1, −1, 2), it contains these points as well
so that
3a + 3b – c = 0
and 3a + b + 0 = 0
Solving we get

and thus the equation of the plane is
(x + 2) - 3(y + 2) = 0
x+3y-4=0

Intercepts on axes = 4, 4/3
The required sum= 4+(4/3)=16/3
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Most Upvoted Answer
The plane passing through the point (−2, −2, 2) and contai...

Given Information:
- Plane passes through the point (-2, -2, 2)
- Plane contains the line joining the points (1, 1, 1) and (1, -1, 2)

Calculating the Equation of the Plane:
- The direction vector of the line joining the two points is (0, -2, 1)
- The normal vector of the plane is perpendicular to the direction vector, so it is parallel to (0, -2, 1)
- Using the point (-2, -2, 2) and the normal vector (0, -2, 1), we can find the equation of the plane as 0(x+2) - 2(y+2) + 1(z-2) = 0

Calculating Intercepts:
- To find the x-intercept, set y = 0 and z = 0 in the equation of the plane: x = -1
- To find the y-intercept, set x = 0 and z = 0 in the equation of the plane: y = -1
- To find the z-intercept, set x = 0 and y = 0 in the equation of the plane: z = 2

Sum of the Lengths of Intercepts:
- Length of x-intercept = 1
- Length of y-intercept = 1
- Length of z-intercept = 2
- Sum of lengths = 1 + 1 + 2 = 4

Therefore, the sum of the lengths of the intercepts on the coordinate axes is 4, which corresponds to option D.
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The plane passing through the point (−2, −2, 2) and containing the line joining the points(1, 1, 1) and (1, −1, 2) makes intercepts on the coordinates axes then sum of the lengths of intercepts isa)3b)4c)6d)12Correct answer is option 'D'. Can you explain this answer?
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The plane passing through the point (−2, −2, 2) and containing the line joining the points(1, 1, 1) and (1, −1, 2) makes intercepts on the coordinates axes then sum of the lengths of intercepts isa)3b)4c)6d)12Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The plane passing through the point (−2, −2, 2) and containing the line joining the points(1, 1, 1) and (1, −1, 2) makes intercepts on the coordinates axes then sum of the lengths of intercepts isa)3b)4c)6d)12Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The plane passing through the point (−2, −2, 2) and containing the line joining the points(1, 1, 1) and (1, −1, 2) makes intercepts on the coordinates axes then sum of the lengths of intercepts isa)3b)4c)6d)12Correct answer is option 'D'. Can you explain this answer?.
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