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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?
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 the x and y axes respectively.
Calculating the Angle with the Z-axis:
When a line makes angles α, β, and γ with the positive directions of the x, y, and z axes respectively, then the angle θ that the line makes with the positive direction of the z-axis can be calculated using the formula:
cos²(θ) = cos²(α) + cos²(β) + cos²(γ)
In this case, α = 45°, β = 60°, and γ = θ (the angle we need to find).
Plugging in the values:
cos²(θ) = cos²(45°) + cos²(60°)
cos²(θ) = (1/√2)² + (1/2)²
cos²(θ) = 1/2 + 1/4
cos²(θ) = 3/4
Taking the square root of both sides:
cos(θ) = √(3/4)
cos(θ) = √3/2
Thus, the angle the line makes with the positive direction of the z-axis is 60°.
Therefore, the correct answer is option A) 60°.
- The line makes angles of 45° and 60° with the positive directions of the x and y axes respectively.
Calculating the Angle with the Z-axis:
When a line makes angles α, β, and γ with the positive directions of the x, y, and z axes respectively, then the angle θ that the line makes with the positive direction of the z-axis can be calculated using the formula:
cos²(θ) = cos²(α) + cos²(β) + cos²(γ)
In this case, α = 45°, β = 60°, and γ = θ (the angle we need to find).
Plugging in the values:
cos²(θ) = cos²(45°) + cos²(60°)
cos²(θ) = (1/√2)² + (1/2)²
cos²(θ) = 1/2 + 1/4
cos²(θ) = 3/4
Taking the square root of both sides:
cos(θ) = √(3/4)
cos(θ) = √3/2
Thus, the angle the line makes with the positive direction of the z-axis is 60°.
Therefore, the correct answer is option A) 60°.
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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
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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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