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In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z – 1 = 0
  • a)
    The planes are perpendicular
  • b)
    The planes are parallel
  • c)
    The planes are at 45
  • d)
    The planes are at 55
Correct answer is option 'B'. Can you explain this answer?
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In the following case, determine whether the given planes are parallel...
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In the following case, determine whether the given planes are parallel...
Given,2,three dimensional planes.

2x-2y+4z+5=0
3x-3y+6z-1=0

If their corresponding elemental ratios are equal then the planes are said to be parallel planes.So,,,

Comparing

2/3=2/3=2/3 {a1/b1=a2/b2=a3/b3}
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In the following case, determine whether the given planes are parallel...
Explanation:

Given Planes:
1. 2x - 2y + 4z + 5 = 0
2. 3x - 3y + 6z - 1 = 0

Comparing Coefficients:
- To determine if the planes are parallel or perpendicular, we compare the normal vectors of the planes.
- Normal vector of plane 1: <2, -2,="" 4="">
- Normal vector of plane 2: <3, -3,="" 6="">

Angle Calculation:
- The dot product of two vectors is given by: A . B = |A| |B| cos(theta)
- If the dot product is 0, the planes are perpendicular. If the dot product is a non-zero constant, the planes are parallel.
- Calculating the dot product: <2, -2,="" 4=""> . <3, -3,="" 6=""> = 2*3 + (-2)(-3) + 4*6 = 6 + 6 + 24 = 36

Conclusion:
- Since the dot product is non-zero, the planes are parallel to each other.
Therefore, the correct answer is option B, the planes are parallel.
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In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z – 1 = 0a)The planes are perpendicularb)The planes are parallelc)The planes are at45∘d)The planes are at55∘Correct answer is option 'B'. Can you explain this answer?
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