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Equation of a line passing through point (1, 1, 1) and parallel to z-axis is
A line parallel to the z-axis has constant x and y coordinates, while the z-coordinate changes. For a line passing through the point (1, 1, 1) and parallel to the z-axis, the x and y coordinates remain constant at 1, while the z-coordinate changes. The parametric equation of the line is: (x - 1)/0 =Read more
A line parallel to the z-axis has constant x and y coordinates, while the z-coordinate changes. For a line passing through the point (1, 1, 1) and parallel to the z-axis, the x and y coordinates remain constant at 1, while the z-coordinate changes.
The parametric equation of the line is:
(x – 1)/0 = (y – 1)/0 = (z – 1)/1
Thus, the correct answer is:
(x – 1)/0 = (y – 1)/0 = (z – 1)/1
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If n(A) = 10, n (B) = 6, n(C) = 5 for three disjoints sets A, B and C, then n (A ∪ B ∪ C) =
Choice (a). is correct. As A, B and C are disjoints sets. n(A ∪ B ∪ C) = n (A) +n(B) +n(C) = 10 + 6 + 5 = 21 This question related to Chapter 1 maths Class 11th NCERT. From the Chapter 1. Sets. Give answer according to your understanding. For more please visit here: https://www.tiwariacademy.com/nceRead more
Choice (a). is correct. As A, B and C are disjoints sets. n(A ∪ B ∪ C) = n (A) +n(B) +n(C) = 10 + 6 + 5 = 21
This question related to Chapter 1 maths Class 11th NCERT. From the Chapter 1. Sets. Give answer according to your understanding.
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The angle between the lines 2x = 3y = -z and 6x = -y = -4z is
The given equations of the lines can be written in parametric form: For the first line: 2x = 3y = -z, let the parameter be t. x = t/2, y = t/3, z = -t. For the second line: 6x = -y = -4z, let the parameter be s. x = s/6, y = -s, z = -s/4. The direction ratios of the first line are (1/2, 1/3, -1) andRead more
The given equations of the lines can be written in parametric form:
For the first line:
2x = 3y = -z, let the parameter be t.
x = t/2, y = t/3, z = -t.
For the second line:
6x = -y = -4z, let the parameter be s.
x = s/6, y = -s, z = -s/4.
The direction ratios of the first line are (1/2, 1/3, -1) and the direction ratios of the second line are (1/6, -1, -1/4).
The angle θ between two lines is given by the formula:
cos θ = (l₁l₂ + m₁m₂ + n₁n₂) / √(l₁² + m₁² + n₁²) * √(l₂² + m₂² + n₂²)
Substitute the values:
cos θ = [(1/2)(1/6) + (1/3)(-1) + (-1)(-1/4)] / √[(1/2)² + (1/3)² + (-1)²] * √[(1/6)² + (-1)² + (-1/4)²]
Simplifying this expression results in cos θ = 0, so the angle θ = 90°.
Thus, the correct answer is: 90°
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If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are
The direction cosines of a line are the cosines of the angles it makes with the x, y, and z axes. Given the angles: - θ₁ = 90° with the x-axis, so cos(θ₁) = 0 - θ₂ = 135° with the y-axis, so cos(θ₂) = -1/√2 - θ₃ = 45° with the z-axis, so cos(θ₃) = 1/√2 Thus, the direction cosines are: 0, -1/√2, 1/√2Read more
The direction cosines of a line are the cosines of the angles it makes with the x, y, and z axes.
Given the angles:
– θ₁ = 90° with the x-axis, so cos(θ₁) = 0
– θ₂ = 135° with the y-axis, so cos(θ₂) = -1/√2
– θ₃ = 45° with the z-axis, so cos(θ₃) = 1/√2
Thus, the direction cosines are:
0, -1/√2, 1/√2
Therefore, the correct answer is:
0, -1/√2, 1/√2
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The angle between the lines whose direction ratios are proportional to a², b², c² and b² – c², c² – a², a² – b² is
The direction ratios of the two lines are given as: Line 1: a², b², c² Line 2: b² - c², c² - a², a² - b² The angle θ between two lines is given by the formula: cos θ = (l₁l₂ + m₁m₂ + n₁n₂) / √(l₁² + m₁² + n₁²) * √(l₂² + m₂² + n₂²) Substituting the direction ratios into the formula: cos θ = [(a²)(b²Read more
The direction ratios of the two lines are given as:
Line 1: a², b², c²
Line 2: b² – c², c² – a², a² – b²
The angle θ between two lines is given by the formula:
cos θ = (l₁l₂ + m₁m₂ + n₁n₂) / √(l₁² + m₁² + n₁²) * √(l₂² + m₂² + n₂²)
Substituting the direction ratios into the formula:
cos θ = [(a²)(b² – c²) + (b²)(c² – a²) + (c²)(a² – b²)] / √[(a²)² + (b²)² + (c²)²] * √[(b² – c²)² + (c² – a²)² + (a² – b²)²]
After simplifying the expression, we get cos θ = 0, which means θ = π/2.
Thus, the correct answer is: π/2
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