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In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.
2x + 3y + 4z – 12 = 0
Concept: undefined >> undefined
In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.
3y + 4z – 6 = 0
Concept: undefined >> undefined
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In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.
x + y + z = 1
Concept: undefined >> undefined
In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.
5y + 8 = 0
Concept: undefined >> undefined
Find the vector and Cartesian equation of the planes that passes through the point (1, 0, −2) and the normal to the plane is `hati + hatj - hatk`
Concept: undefined >> undefined
Find the vector and Cartesian equation of the planes that passes through the point (1, 4, 6) and the normal vector to the plane is `hati -2hatj + hatk`
Concept: undefined >> undefined
Show that all the diagonal elements of a skew symmetric matrix are zero.
Concept: undefined >> undefined
Find the equation of the plane through the line of intersection of `vecr*(2hati-3hatj + 4hatk) = 1`and `vecr*(veci - hatj) + 4 =0`and perpendicular to the plane `vecr*(2hati - hatj + hatk) + 8 = 0`. Hence find whether the plane thus obtained contains the line x − 1 = 2y − 4 = 3z − 12.
Concept: undefined >> undefined
If y = sin (sin x), prove that `(d^2y)/(dx^2) + tan x dy/dx + y cos^2 x = 0`
Concept: undefined >> undefined
If A and B are symmetric matrices of the same order, write whether AB − BA is symmetric or skew-symmetric or neither of the two.
Concept: undefined >> undefined
Write a square matrix which is both symmetric as well as skew-symmetric.
Concept: undefined >> undefined
If \[A = \begin{bmatrix}1 & 2 \\ 0 & 3\end{bmatrix}\] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then B is equal to.
Concept: undefined >> undefined
For what value of x, is the matrix \[A = \begin{bmatrix}0 & 1 & - 2 \\ - 1 & 0 & 3 \\ x & - 3 & 0\end{bmatrix}\] a skew-symmetric matrix?
Concept: undefined >> undefined
If a matrix A is both symmetric and skew-symmetric, then
Concept: undefined >> undefined
The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is
Concept: undefined >> undefined
If A is a square matrix, then AA is a
Concept: undefined >> undefined
If A and B are symmetric matrices, then ABA is
Concept: undefined >> undefined
If A = [aij] is a square matrix of even order such that aij = i2 − j2, then
Concept: undefined >> undefined
If \[A = \begin{bmatrix}2 & 0 & - 3 \\ 4 & 3 & 1 \\ - 5 & 7 & 2\end{bmatrix}\] is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is
Concept: undefined >> undefined
If A and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A − 2B is
Concept: undefined >> undefined
