Find the equation of the plane which is parallel to the x-axis and has intercepts 5 and 7 on the y and z-axis, respectively.

Solution

Let the equation of plane be

straight x over straight a plus straight y over straight b plus straight z over straight c equals 1

...(1)
Here b = 5, c = 7 ...(2)
Since the plane is parallel to x-axis whose direction ratios are 1, 0, 0
∴ normal to the plane must be perpendicular to the x-axis. But the direction ratios of the normal to the plane are

1 over straight a comma space 1 over straight b comma space 1 over straight c.

therefore space space space space 1 over straight a cross times 1 plus space 1 over straight b cross times 0 space plus space 1 over straight c cross times 0 space equals space 0 space space space space space space space rightwards double arrow space space space space space 1 over straight a space equals space 0

...(3)
From (1) and (2), (3), we have

straight y over 5 plus straight z over 7 space equals space 1 space space space space or space space 7 straight y space plus space 5 straight z space equals space 35

which is required equation of plane.

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Three Dimensional Geometry

Find the equation of the plane which is parallel to the x-axis and has intercepts 5 and 7 on the y and z-axis, respectively.

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin²α + sin² β + sin²γ = 2.

Show that the points A(2, 3, – 4), B(1, –2, 3) and C (3, 8, –11) are collinear.

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For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

Find the equation of the plane which is parallel to the x-axis and has intercepts 5 and 7 on the y and z-axis, respectively.

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin2α + sin2 β + sin2γ = 2.

Show that the points A(2, 3, – 4), B(1, –2, 3) and C (3, 8, –11) are collinear.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If α, β, γ are the angles which a line makes with the axes, prove that sin²α + sin² β + sin²γ = 2.