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A line makes angles of 45° and 60° with the positive directions of x and y axes respectively. An angle, which the line can make with the positive direction of z-axis is:
- a)60°
- b)40°
- c)80°
- d)100°
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A line makes angles of 45° and 60° with the positive direction...
Let α , β , γ be the angles, which the line makes with the positive directions of x-axis, y-axis and z-axis respectively
Hence the line makes an angle of 60° with the positive direction of z-axis
Hence the line makes an angle of 60° with the positive direction of z-axis
Most Upvoted Answer
A line makes angles of 45° and 60° with the positive direction...
Given information:
- The line makes angles of 45° and 60° with the positive directions of x and y axes respectively.
Explanation:
- Let's consider the line in the first quadrant, making an angle of 45° with the x-axis and 60° with the y-axis.
- We can visualize this as a line that lies in the xy-plane, with a component along the x-axis and y-axis.
- The angle the line makes with the positive z-axis can be found using trigonometry.
- The angle θ the line makes with the positive z-axis is given by:
tan(θ) = (component along z-axis)/(component in xy-plane)
- tan(θ) = tan(60°)/tan(45°)
- tan(θ) = √3 / 1
- θ = tan^(-1)(√3) ≈ 60°
Conclusion:
- Therefore, the angle the line can make with the positive direction of the z-axis is approximately 60°.
- Hence, the correct answer is option 'A) 60°'.
- The line makes angles of 45° and 60° with the positive directions of x and y axes respectively.
Explanation:
- Let's consider the line in the first quadrant, making an angle of 45° with the x-axis and 60° with the y-axis.
- We can visualize this as a line that lies in the xy-plane, with a component along the x-axis and y-axis.
- The angle the line makes with the positive z-axis can be found using trigonometry.
- The angle θ the line makes with the positive z-axis is given by:
tan(θ) = (component along z-axis)/(component in xy-plane)
- tan(θ) = tan(60°)/tan(45°)
- tan(θ) = √3 / 1
- θ = tan^(-1)(√3) ≈ 60°
Conclusion:
- Therefore, the angle the line can make with the positive direction of the z-axis is approximately 60°.
- Hence, the correct answer is option 'A) 60°'.
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A line makes angles of 45° and 60° with the positive directions of x and y axes respectively. An angle, which the line can make with the positive direction of z-axis is:a)60°b)40°c)80°d)100°Correct answer is option 'A'. Can you explain this answer?
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