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

Projection vector of `vec"a"` on `vec"b"` is ______.

Find: `int (sin2x)/sqrt(9 - cos^4x) dx`

The scalar projection of the vector `3hati - hatj - 2hatk` on the vector `hati + 2hatj - 3hatk` is ______.

If `veca` and `vecb` are two vectors such that `|veca + vecb| = |vecb|`, then prove that `(veca + 2vecb)` is perpendicular to `veca`.

If `veca` and `vecb` are unit vectors and θ is the angle between them, then prove that `sin  θ/2 = 1/2 |veca  - vecb|`.

Write the projection of the vector `(vecb + vecc)` on the vector `veca`, where `veca = 2hati - 2hatj + hatk, vecb = hati + 2hatj - 2hatk` and `vecc = 2hati - hatj + 4hatk`.

Projection of vector `2hati + 3hatj` on the vector `3hati - 2hatj` is ______.

A unit vector `hata` makes equal but acute angles on the coordinate axes. The projection of the vector `hata` on the vector `vecb = 5hati + 7hatj - hatk` is ______.

If `veca, vecb, vecc` are mutually perpendicular vectors of equal magnitudes, show that the vector `vecc* vecd = 15` is equally inclined to `veca, vecb "and"  vecc.` 

Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane `vec r.(hati+hatj+hatk)=2`

Find the vector equation of the plane which contains the line of intersection of the planes `vecr (hati+2hatj+3hatk)-4=0` and `vec r (2hati+hatj-hatk)+5=0` which is perpendicular to the plane.`vecr(5hati+3hatj-6hatk)+8=0`

Find the vector equation of the plane passing through three points with position vectors ` hati+hatj-2hatk , 2hati-hatj+hatk and hati+2hatj+hatk` . Also find the coordinates of the point of intersection of this plane and the line `vecr=3hati-hatj-hatk lambda +(2hati-2hatj+hatk)`

Find the vector equation of the plane with intercepts 3, –4 and 2 on x, y and z-axis respectively.

The two adjacent sides of a parallelogram are `2hati-4hatj-5hatk and 2 hati+2hatj+3hatj` . Find the two unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram.

Find the equation of the plane which contains the line of intersection of the planes

`vecr.(hati-2hatj+3hatk)-4=0" and"`

`vecr.(-2hati+hatj+hatk)+5=0`

and whose intercept on x-axis is equal to that of on y-axis.

Matrix A = `[(0,2b,-2),(3,1,3),(3a,3,-1)]`is given to be symmetric, find values of a and b

Find the vector equation of a plane which is at a distance of 5 units from the origin and its normal vector is `2hati-3hatj+6hatk`

If A= `((3,5),(7,9))`is written as A = P + Q, where P is a symmetric matrix and Q is skew symmetric matrix, then write the matrix P.

If A is a skew symmetric matric of order 3, then prove that det A  = 0

The x-coordinate of a point of the line joining the points P(2,2,1) and Q(5,1,-2) is 4. Find its z-coordinate