Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

The equations of x-axis in space are ______.

Find the equation of a plane which is at a distance `3sqrt(3)` units from origin and the normal to which is equally inclined to coordinate axis.

If the line drawn from the point (–2, – 1, – 3) meets a plane at right angle at the point (1, – 3, 3), find the equation of the plane.

The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1(α) with x-axis. The value of α is equal to ______.

The unit vector normal to the plane x + 2y +3z – 6 = 0 is `1/sqrt(14)hat"i" + 2/sqrt(14)hat"j" + 3/sqrt(14)hat"k"`.

If A, B are non-singular square matrices of the same order, then (AB^–1)^–1 = ______.

If `veca = hati + hatj + hatk, veca.vecb` = 1 and `veca xx vecb = hatj - hatk`, then find `|vecb|`.

If A and B are invertible square matrices of the same order, then which of the following is not correct?

The two vectors `hatj+hatk " and " 3hati-hatj+4hatk` represent the two sides AB and AC, respectively of a ∆ABC. Find the length of the median through A

Find `int (sin^2 x - cos^2 x)/(sin xcosx) dx`

Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector.`3hati + 5hatj - 6hatk`

Find the equations of the planes that passes through three points.

(1, 1, −1), (6, 4, −5), (−4, −2, 3)

Find the equations of the planes that passes through three points.

(1, 1, 0), (1, 2, 1), (−2, 2, −1)

Find the equation of the plane passing through (a, b, c) and parallel to the plane `vecr.(hati + hatj + hatk) = 2`

Find the equation of the plane passing through the point (−1, 3, 2) and perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0.

If the points (1, 1, p) and (−3, 0, 1) be equidistant from the plane `vecr.(3hati + 4hatj - 12hatk)+ 13 = 0`, then find the value of p.

If O be the origin and the coordinates of P be (1, 2, −3), then find the equation of the plane passing through P and perpendicular to OP.

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes `vecr = (hati - hatj + 2hatk)  = 5`and `vecr.(3hati + hatj + hatk) = 6`

Find the vector equation of the line passing through the point (1, 2, − 4) and perpendicular to the two lines: 

`(x -8)/3 = (y+19)/(-16) = (z - 10)/7 and (x - 15)/3 = (y - 29)/8 = (z- 5)/(-5)`

If `tan^(-1)  (x- 3)/(x - 4) + tan^(-1)  (x +3)/(x + 4) = pi/4`, then find the value of x.