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Angle Between two Planes Video Lecture | Mathematics (Maths) for JEE Main & Advanced
FAQs on Angle Between two Planes Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. What is the formula to find the angle between two planes? |  |
Ans. The formula to find the angle between two planes is given by:
\[ \cos \theta = \frac{{a_1a_2 + b_1b_2 + c_1c_2}}{{\sqrt{{a_1^2 + b_1^2 + c_1^2}} \sqrt{{a_2^2 + b_2^2 + c_2^2}}}} \]
where \( (a_1, b_1, c_1) \) and \( (a_2, b_2, c_2) \) are the normal vectors of the two planes.
| 2. How can we find the normal vectors of the given planes to calculate the angle between them? | |
Ans. To find the normal vectors of the given planes, we can use the coefficients of \( x, y, \) and \( z \) in the equation of the planes. The normal vector will have components as \( (a, b, c) \) where the equation of the plane is \( ax + by + cz = d \).
| 3. Can the angle between two planes be negative? | |
Ans. No, the angle between two planes is always measured as the acute angle between their normal vectors. Therefore, the angle between two planes is always a positive value between \( 0^\circ \) and \( 180^\circ \).
| 4. How do we interpret the angle between two planes in 3D space? | |
Ans. The angle between two planes in 3D space indicates how much the two planes are tilted or inclined towards each other. A smaller angle implies that the planes are closer to being parallel, while a larger angle indicates they are more inclined or intersecting at a steeper angle.
| 5. Can we use the formula to find the angle between two planes in any coordinate system? | |
Ans. Yes, the formula to find the angle between two planes is applicable in any coordinate system as long as the normal vectors of the planes are known. The formula calculates the angle based on the dot product of the normal vectors and their magnitudes.
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