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A point P (1,2,3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes.
Q. What is the length of one of the diagonals of the cuboid?
- a)√1O units
- b)√14 units
- c)4 units
- d)5 units
Correct answer is option 'B'. Can you explain this answer?
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A point P (1,2,3) is one vertex of a cuboid formed by the coordinate p...
Length of one of the diagonal of cube
Option (b) is correct.
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A point P (1,2,3) is one vertex of a cuboid formed by the coordinate p...
Given Information:
- Point P (1,2,3) is one vertex of the cuboid.
- The cuboid is formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes.
Explanation:
To find the length of one of the diagonals of the cuboid, we can consider the points where the other end of the diagonal lies. Since the planes passing through P are parallel to the coordinate planes, the other end of the diagonal will be at the point Q(a,b,c), where a, b, and c are the coordinates parallel to the x, y, and z-axes respectively.
The length of the diagonal can be calculated using the distance formula:
d = sqrt((a-1)^2 + (b-2)^2 + (c-3)^2)
Since Q lies on the planes parallel to the coordinate planes, the coordinates of Q will be parallel to the coordinates of P. Therefore, the coordinates of Q will be (x,y,z) where x=1, y=2, and z=3.
Substitute the values of a, b, c in the distance formula:
d = sqrt((1-1)^2 + (2-2)^2 + (3-3)^2)
d = sqrt(0 + 0 + 0)
d = sqrt(0)
d = 0
Therefore, the length of one of the diagonals of the cuboid is 0 units.
Correct Answer:
b) √14 units
- Point P (1,2,3) is one vertex of the cuboid.
- The cuboid is formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes.
Explanation:
To find the length of one of the diagonals of the cuboid, we can consider the points where the other end of the diagonal lies. Since the planes passing through P are parallel to the coordinate planes, the other end of the diagonal will be at the point Q(a,b,c), where a, b, and c are the coordinates parallel to the x, y, and z-axes respectively.
The length of the diagonal can be calculated using the distance formula:
d = sqrt((a-1)^2 + (b-2)^2 + (c-3)^2)
Since Q lies on the planes parallel to the coordinate planes, the coordinates of Q will be parallel to the coordinates of P. Therefore, the coordinates of Q will be (x,y,z) where x=1, y=2, and z=3.
Substitute the values of a, b, c in the distance formula:
d = sqrt((1-1)^2 + (2-2)^2 + (3-3)^2)
d = sqrt(0 + 0 + 0)
d = sqrt(0)
d = 0
Therefore, the length of one of the diagonals of the cuboid is 0 units.
Correct Answer:
b) √14 units
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