Find the equation of the plane through the intersection of the planes 3x – y + 2z – 4 = 0 and x + y + z – 2 = 0 and the point (2, 2, 1).
[11] Three - Dimensional Geometry
Chapter: [11] Three - Dimensional Geometry
Concept: undefined >> undefined
Find the vector equation of the plane passing through the intersection of the planes `vecr.(2hati + 2hatj - 3hatk) = 7, vecr.(2hati + 5hatj + 3hatk) = 9` and through the point (2, 1, 3)
[11] Three - Dimensional Geometry
Chapter: [11] Three - Dimensional Geometry
Concept: undefined >> undefined
Find the equation of the plane passing through the line of intersection of the planes `vecr.(hati + hatj + hatk) = 1` and `vecr.(2hati + 3hatj -hatk) + 4 = 0` and parallel to x-axis.
[11] Three - Dimensional Geometry
Chapter: [11] Three - Dimensional Geometry
Concept: undefined >> undefined
Find the equation of the plane which contains the line of intersection of the planes `vecrr.(hati + 2hatj + 3hatk) - 4 = 0, vecr.(2hati + htj - hatk) + 5 = 0`, and which is perpendicular to the plane `vecr.(5hati + 3hatj - 6hatk) + 8 = 0`.
[11] Three - Dimensional Geometry
Chapter: [11] Three - Dimensional Geometry
Concept: undefined >> undefined
Using vectors find the area of triangle ABC with vertices A(1, 2, 3), B(2, −1, 4) and C(4, 5, −1).
[10] Vectors
Chapter: [10] Vectors
Concept: undefined >> undefined
Express the following matrix as the sum of a symmetric and skew-symmetric matrix and verify your result:
\[\begin{bmatrix}3 & - 2 & - 4 \\ 3 & - 2 & - 5 \\ - 1 & 1 & 2\end{bmatrix}\]
[3] Matrices
Chapter: [3] Matrices
Concept: undefined >> undefined
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{x - 1}{\sqrt{x + 4}} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{x}{\sqrt{x + 4}} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\sqrt{\frac{1 - \cos x}{1 + \cos x}} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
Evaluate the following integrals:
`int "sec x"/"sec 2x" "dx"`
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{\cos 2x}{\left( \cos x + \sin x \right)^2} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{1 + \tan x}{1 - \tan x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{1}{x \log x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{1}{e^x + 1} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
` ∫ {cot x}/ { log sin x} dx `
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{e^{2x}}{e^{2x} - 2} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{2 \cos x - 3 \sin x}{6 \cos x + 4 \sin x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{\cos 2x + x + 1}{x^2 + \sin 2x + 2x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{1}{\cos\left( x + a \right) \cos\left( x + b \right)}dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
