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The distance of the point (2, 3, 4) from the plane 3x - 6y + 2z + 11 =0 is
- a)1
- b)43/√7
- c)1/49
- d)-1/49
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The distance of the point (2,3,4) from the plane 3x - 6y + 2z + 11 =0 ...
Proof: If d is the required distance of the point (2, 3, 4) from the plane
3x -6y + 2z + 11 = 0
Then
3x -6y + 2z + 11 = 0
Then
Most Upvoted Answer
The distance of the point (2,3,4) from the plane 3x - 6y + 2z + 11 =0 ...
Proof: If d is the required distance of the point (2, 3, 4) from the plane
3x -6y + 2z + 11 = 0
Then
3x -6y + 2z + 11 = 0
Then
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Community Answer
The distance of the point (2,3,4) from the plane 3x - 6y + 2z + 11 =0 ...
Distance of a Point from a Plane
Given:
Point P(2,3,4)
Plane equation: 3x - 6y + 2z + 11 = 0
Formula:
The distance between a point (x,y,z) and a plane Ax + By + Cz + D = 0 is given by:
Distance = |Ax + By + Cz + D| / √(A^2 + B^2 + C^2)
Calculations:
- Substitute the values of the point coordinates and the coefficients of the plane equation into the formula:
Distance = |3(2) - 6(3) + 2(4) + 11| / √(3^2 + (-6)^2 + 2^2)
Distance = |6 - 18 + 8 + 11| / √(9 + 36 + 4)
Distance = |7| / √49
Distance = 7 / 7
Distance = 1
Therefore, the distance of the point (2,3,4) from the plane 3x - 6y + 2z + 11 = 0 is 1. Hence, the correct answer is option 'A'.
Given:
Point P(2,3,4)
Plane equation: 3x - 6y + 2z + 11 = 0
Formula:
The distance between a point (x,y,z) and a plane Ax + By + Cz + D = 0 is given by:
Distance = |Ax + By + Cz + D| / √(A^2 + B^2 + C^2)
Calculations:
- Substitute the values of the point coordinates and the coefficients of the plane equation into the formula:
Distance = |3(2) - 6(3) + 2(4) + 11| / √(3^2 + (-6)^2 + 2^2)
Distance = |6 - 18 + 8 + 11| / √(9 + 36 + 4)
Distance = |7| / √49
Distance = 7 / 7
Distance = 1
Therefore, the distance of the point (2,3,4) from the plane 3x - 6y + 2z + 11 = 0 is 1. Hence, the correct answer is option 'A'.
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