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The direction cosines of the line equally inclined with the axes, are:
- a)1, 1, 1,
- b)0, 0, 0
- c)1/3, 1/3, 1/3
- d)1/√3, 1/√3, 1/√3
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The direction cosines of the line equally inclined with the axes, are:...
Direction cosines are the ratios of the direction ratios of a line. In other words, they represent the cosines of the angles that the line makes with the positive x, y, and z axes.
Let's consider a line equally inclined with the axes. This means that the line makes equal angles with each axis.
To find the direction cosines of this line, we need to determine the cosines of the angles it makes with the x, y, and z axes.
Let's assume that the line makes an angle of θ with each axis. Since the line is equally inclined with the axes, all the angles are equal.
Let's calculate the direction cosine along the x-axis:
cos(θ) = adjacent side / hypotenuse
cos(θ) = 1 / hypotenuse
hypotenuse = 1 / cos(θ)
Similarly, the direction cosine along the y-axis and z-axis would also be 1 / cos(θ).
Therefore, the direction cosines of the line equally inclined with the axes are (1 / cos(θ), 1 / cos(θ), 1 / cos(θ)).
Since the line is equally inclined with the axes, the angle θ is the same for all three direction cosines.
Hence, the correct answer is option D: 1/3, 1/3, 1/3.
Let's consider a line equally inclined with the axes. This means that the line makes equal angles with each axis.
To find the direction cosines of this line, we need to determine the cosines of the angles it makes with the x, y, and z axes.
Let's assume that the line makes an angle of θ with each axis. Since the line is equally inclined with the axes, all the angles are equal.
Let's calculate the direction cosine along the x-axis:
cos(θ) = adjacent side / hypotenuse
cos(θ) = 1 / hypotenuse
hypotenuse = 1 / cos(θ)
Similarly, the direction cosine along the y-axis and z-axis would also be 1 / cos(θ).
Therefore, the direction cosines of the line equally inclined with the axes are (1 / cos(θ), 1 / cos(θ), 1 / cos(θ)).
Since the line is equally inclined with the axes, the angle θ is the same for all three direction cosines.
Hence, the correct answer is option D: 1/3, 1/3, 1/3.
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The direction cosines of the line equally inclined with the axes, are:...
Cos^2 alpha+cos ^2 beta +cos^ 2 gamma =1
put alpha =beta. =gamma
we get cosalpha= 1/√3
DC's of given line (1/√3,1/√3,1/3)
put alpha =beta. =gamma
we get cosalpha= 1/√3
DC's of given line (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, 1,b)0, 0, 0c)1/3, 1/3, 1/3d)1/√3, 1/√3, 1/√3Correct answer is option 'D'. Can you explain this answer?
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