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 – 1 = 0 and 2x – y + 3z + 3 = 0

Solution

The given planes are
2x – + 3z – 1 = 0 ...(1)
and 2x – y + 3z + 3 = 0 ...(2)
Direction ratios of normal to plane (1) are 2, –1, 3.
Direction ratios of normal to plane (2) are 2, – 1, 3.
Now, $2 over 2 space equals space fraction numerator negative 1 over denominator negative 1 end fraction equals 3 over 3$
∴ given planes (1) and (2) are parallel.

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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 – 1 = 0 and 2x – y + 3z + 3 = 0

Some More Questions From Three Dimensional Geometry Chapter

Find the direction cosines of x, y and z-axis.

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 – 1 = 0 and 2x – y + 3z + 3 = 0

Some More Questions From Three Dimensional Geometry Chapter

Find the direction cosines of x, y and z-axis.

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 – 1 = 0 and 2x – y + 3z + 3 = 0