Arts (English Medium) Class 12 - CBSE Question Bank Solutions

Find the values of x, y, z if the matrix `A = [(0,2y,z),(x,y,-z),(x , -y,z)]` satisfy the equation A'A = I.

If the matrix A is both symmetric and skew symmetric, then ______.

Find the Cartesian equation of the following planes:

`vecr.(hati + hatj-hatk) = 2`

Find the Cartesian equation of the following planes:

`vecr.(2hati + 3hatj-4hatk) = 1`

Find the Cartesian equation of the following planes:

`vecr.[(s-2t)hati + (3 - t)hatj + (2s + t)hatk] = 15`

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.

2x + 3y + 4z – 12 = 0

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.

3y + 4z – 6 = 0

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.

x + y + z = 1

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.

5y + 8 = 0

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`

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`

Show that all the diagonal elements of a skew symmetric matrix are zero.

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.

If y = sin (sin x), prove that `(d^2y)/(dx^2) + tan x dy/dx + y cos^2 x = 0`

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.

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?

If a matrix A is both symmetric and skew-symmetric, then

The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is