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The direction cosines of the line equally inclined with the axes are:
- a)1, 1, 1
- b)± 1/√3, 1/√3, 1/√3
- c)1, 0, 0
- d)1/3, 1/3, 1/3
Correct answer is option 'B'. Can you explain this answer?
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The direction cosines of the line equally inclined with the axes are:...
Direction Cosines of a Line Equally Inclined with the Axes
Definition:
Direction cosines of a line are the cosines of the angles that the line makes with the positive x, y, and z-axes.
Explanation:
When a line is equally inclined with the axes, it means that the line makes the same angle with each of the three axes.
Calculation:
Let the angle that the line makes with each axis be θ. Since the line is equally inclined with the axes, θ is the same for all three axes.
The direction cosines of the line can be calculated using the formulas:
l = cos(θ), m = cos(θ), n = cos(θ)
Since θ is the same for all three axes, the direction cosines will be equal.
Therefore, the direction cosines of the line are ± cos(θ), cos(θ), cos(θ).
Correct Answer:
Option B: ± 1/√3, 1/√3, 1/√3
In this case, cos(θ) = 1/√3, which gives the direction cosines as ± 1/√3, 1/√3, 1/√3.
Definition:
Direction cosines of a line are the cosines of the angles that the line makes with the positive x, y, and z-axes.
Explanation:
When a line is equally inclined with the axes, it means that the line makes the same angle with each of the three axes.
Calculation:
Let the angle that the line makes with each axis be θ. Since the line is equally inclined with the axes, θ is the same for all three axes.
The direction cosines of the line can be calculated using the formulas:
l = cos(θ), m = cos(θ), n = cos(θ)
Since θ is the same for all three axes, the direction cosines will be equal.
Therefore, the direction cosines of the line are ± cos(θ), cos(θ), cos(θ).
Correct Answer:
Option B: ± 1/√3, 1/√3, 1/√3
In this case, cos(θ) = 1/√3, which gives the direction cosines as ± 1/√3, 1/√3, 1/√3.
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The direction cosines of the line equally inclined with the axes are:a)1, 1, 1b)± 1/√3, 1/√3, 1/√3c)1, 0, 0d)1/3, 1/3, 1/3Correct answer is option 'B'. Can you explain this answer?
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