Question

hiii guys... please explain how to find angle between two planes...​

Answer 1

Answer:

The angle between two planes is generally calculated with the knowledge of angle between their normal. In other words, the angle between normal to two planes is the angle between the two planes. This can be understood quite clearly from the below figure:

angle between two planes

Let n1→ and n2→ be the two normal to the planes aligned to each other at an angle θ. The equation of two planes can be given by:

r⃗ .n1→ = d1

r⃗ .n2→ = d2

From the above figure, we learnt that the angle between the two planes is equal to the angle between their normal, thus,

angle between two planes

Calculation of Angle Between Two plane in the Cartesian Plane

Let A1 x + B1 y + C1z + D1 = 0 and A2x + B2y + C2 z + D2 = 0 be the equation of two planes aligned to each other at an angle θ where A1, B1, C1 and A2, B2, C2 are the direction ratios of the normal to the planes.

The cosine of the angle between the two planes is given by:

Cartesian form

Angle Between Two Planes Example

Question: Calculate the angle between the two planes given by the equation 2x + 4y – 2z = 5 and 6x – 8y – 2z = 14.

Solution: As learnt above, the angle between two planes is equal to the angle between their normals. Normal vectors to the above planes are represented by:

n1→ = 2i^ + 4j^ – 2k^

n2→ = 6i^ – 8j^ – 2k^