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Two points in cylindrical coordinates are A(ρ = 5, Ø = 700 , z = -3) and B(ρ = 2, Ø = 300 , z = 1) A unit vector at A towards B is
- a)0.03ux - 0.82uy + 0.57uz
- b)0.03ux + 0.82uy + 0.57uz
- c)- 0.03ux + 0.82uy + 0.57uz
- d)0.003ux - 0.82uy + 0.57uz
Correct answer is option 'D'. Can you explain this answer?
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Two points in cylindrical coordinates are A(ρ = 5,Ø =700, z ...
In cartesian coordinates:
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Two points in cylindrical coordinates are A(ρ = 5,Ø =700, z ...
To find the unit vector at point A towards point B, we need to first determine the vector from A to B and then normalize it to obtain the unit vector.
1. Finding the vector from A to B:
The vector from A to B can be obtained by subtracting the coordinates of point A from the coordinates of point B. In cylindrical coordinates, this is done by subtracting the corresponding values of ρ, φ, and z.
ρ_B - ρ_A = 2 - 5 = -3
φ_B - φ_A = 300 - 700 = -400
z_B - z_A = 1 - (-3) = 4
So, the vector from A to B is (-3, -400, 4).
2. Normalizing the vector:
To obtain the unit vector, we divide the vector from A to B by its magnitude.
The magnitude of the vector from A to B can be found using the formula:
|v| = sqrt((ρ_B - ρ_A)^2 + (φ_B - φ_A)^2 + (z_B - z_A)^2)
|v| = sqrt((-3)^2 + (-400)^2 + 4^2)
|v| = sqrt(9 + 160000 + 16)
|v| = sqrt(160025)
|v| ≈ 400.03
Now, we can normalize the vector by dividing each component by its magnitude.
Normalized vector = (-3/400.03, -400/400.03, 4/400.03)
Normalized vector ≈ (-0.0075, -0.9999, 0.0099)
Therefore, the unit vector at point A towards point B is approximately equal to -0.0075ux - 0.9999uy + 0.0099uz.
The correct answer is option 'D' which states: 0.003ux - 0.82uy + 0.57uz. However, this answer does not match the calculations performed above and is incorrect.
1. Finding the vector from A to B:
The vector from A to B can be obtained by subtracting the coordinates of point A from the coordinates of point B. In cylindrical coordinates, this is done by subtracting the corresponding values of ρ, φ, and z.
ρ_B - ρ_A = 2 - 5 = -3
φ_B - φ_A = 300 - 700 = -400
z_B - z_A = 1 - (-3) = 4
So, the vector from A to B is (-3, -400, 4).
2. Normalizing the vector:
To obtain the unit vector, we divide the vector from A to B by its magnitude.
The magnitude of the vector from A to B can be found using the formula:
|v| = sqrt((ρ_B - ρ_A)^2 + (φ_B - φ_A)^2 + (z_B - z_A)^2)
|v| = sqrt((-3)^2 + (-400)^2 + 4^2)
|v| = sqrt(9 + 160000 + 16)
|v| = sqrt(160025)
|v| ≈ 400.03
Now, we can normalize the vector by dividing each component by its magnitude.
Normalized vector = (-3/400.03, -400/400.03, 4/400.03)
Normalized vector ≈ (-0.0075, -0.9999, 0.0099)
Therefore, the unit vector at point A towards point B is approximately equal to -0.0075ux - 0.9999uy + 0.0099uz.
The correct answer is option 'D' which states: 0.003ux - 0.82uy + 0.57uz. However, this answer does not match the calculations performed above and is incorrect.
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Two points in cylindrical coordinates are A(ρ = 5,Ø =700, z = -3) and B(ρ = 2,Ø = 300, z = 1) A unit vector at A towards B isa)0.03ux- 0.82uy+ 0.57uzb)0.03ux+ 0.82uy+ 0.57uzc)- 0.03ux+0.82uy+ 0.57uzd)0.003ux- 0.82uy+ 0.57uzCorrect answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2026 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Two points in cylindrical coordinates are A(ρ = 5,Ø =700, z = -3) and B(ρ = 2,Ø = 300, z = 1) A unit vector at A towards B isa)0.03ux- 0.82uy+ 0.57uzb)0.03ux+ 0.82uy+ 0.57uzc)- 0.03ux+0.82uy+ 0.57uzd)0.003ux- 0.82uy+ 0.57uzCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two points in cylindrical coordinates are A(ρ = 5,Ø =700, z = -3) and B(ρ = 2,Ø = 300, z = 1) A unit vector at A towards B isa)0.03ux- 0.82uy+ 0.57uzb)0.03ux+ 0.82uy+ 0.57uzc)- 0.03ux+0.82uy+ 0.57uzd)0.003ux- 0.82uy+ 0.57uzCorrect answer is option 'D'. Can you explain this answer?.
Two points in cylindrical coordinates are A(ρ = 5,Ø =700, z = -3) and B(ρ = 2,Ø = 300, z = 1) A unit vector at A towards B isa)0.03ux- 0.82uy+ 0.57uzb)0.03ux+ 0.82uy+ 0.57uzc)- 0.03ux+0.82uy+ 0.57uzd)0.003ux- 0.82uy+ 0.57uzCorrect answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2026 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Two points in cylindrical coordinates are A(ρ = 5,Ø =700, z = -3) and B(ρ = 2,Ø = 300, z = 1) A unit vector at A towards B isa)0.03ux- 0.82uy+ 0.57uzb)0.03ux+ 0.82uy+ 0.57uzc)- 0.03ux+0.82uy+ 0.57uzd)0.003ux- 0.82uy+ 0.57uzCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two points in cylindrical coordinates are A(ρ = 5,Ø =700, z = -3) and B(ρ = 2,Ø = 300, z = 1) A unit vector at A towards B isa)0.03ux- 0.82uy+ 0.57uzb)0.03ux+ 0.82uy+ 0.57uzc)- 0.03ux+0.82uy+ 0.57uzd)0.003ux- 0.82uy+ 0.57uzCorrect answer is option 'D'. Can you explain this answer?.
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