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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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Distance of the point (α, β, γ) from yz-plane is
The yz-plane is defined by the equation x = 0, meaning that for any point on the yz-plane, the x-coordinate is 0. The distance of a point (α, β, γ) from the yz-plane is the absolute value of its x-coordinate because the yz-plane is perpendicular to the x-axis. Therefore, the distance of the point (αRead more
The yz-plane is defined by the equation x = 0, meaning that for any point on the yz-plane, the x-coordinate is 0.
The distance of a point (α, β, γ) from the yz-plane is the absolute value of its x-coordinate because the yz-plane is perpendicular to the x-axis.
Therefore, the distance of the point (α, β, γ) from the yz-plane is:|α|
Thus, the correct answer is: |α|
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Which of the following is a true solution? (a) Vinegar solution (b) Blood (c) Milk (d) Muddy water
The correct answer is: (a) Vinegar solution. A true solution is a homogeneous mixture where solute particles are completely dissolved in the solvent and cannot be seen under a microscope. Vinegar is a true solution of acetic acid in water, making it a homogeneous mixture. https://www.tiwariacademy.cRead more
The correct answer is: (a) Vinegar solution. A true solution is a homogeneous mixture where solute particles are completely dissolved in the solvent and cannot be seen under a microscope. Vinegar is a true solution of acetic acid in water, making it a homogeneous mixture.
https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-2/
See lessWhat is the major compound present in common salt? (a) MgCl₂ (b) NaCl (c) CaCl2 (d) KCl
The correct answer is: (b) NaCl. Common salt, also known as table salt, is primarily composed of sodium chloride (NaCl). It is an ionic compound made of sodium (Na⁺) and chloride (Cl⁻) ions, essential for human health and widely used in food and industry. https://www.tiwariacademy.com/ncert-solutionRead more
The correct answer is: (b) NaCl. Common salt, also known as table salt, is primarily composed of sodium chloride (NaCl). It is an ionic compound made of sodium (Na⁺) and chloride (Cl⁻) ions, essential for human health and widely used in food and industry.
https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-2/
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