Three Dimensional Geometry

Question

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them:
2x + y + 3z – 2 = 0 and x – 2y + 5 = 0

Solution

The equations of given planes are
2x + y + 3z – 2 = 0 ...(1)
and x – 2y + 5 = 0 ...(2)
Direction ratios of normal to plane (1) are 2, 1, 3
Direction ratios of normal to plane (2) are 1, – 2, 0.
Now, $2 over 1 not equal to fraction numerator 1 over denominator negative 2 end fraction not equal to 3 over 0$
∴ planes (1) and (2) are not parallel.
Again (2) (1) + (1) (– 2) + (3) (0) = 2 – 2 + 0 = 0
∴ given planes (1) and (2) are perpendicular to each other.

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Three Dimensional Geometry

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them:
2x + y + 3z – 2 = 0 and x – 2y + 5 = 0

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

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For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them:2x + y + 3z – 2 = 0 and x – 2y + 5 = 0

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

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them:
2x + y + 3z – 2 = 0 and x – 2y + 5 = 0

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