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

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

Find the shortest distance between the lines: 

`vecr = (hati+2hatj+hatk) + lambda(hati-hatj+hatk)` and `vecr = 2hati - hatj - hatk + mu(2hati + hatj + 2hatk)`

Find the shortest distance between the lines.

`(x + 1)/7 = (y + 1)/(- 6) = (z + 1)/1` and `(x - 3)/1 = (y - 5)/(- 2) = (z - 7)/1`.

Find the shortest distance between the lines whose vector equations are `vecr = (hati + 2hatj + 3hatk) + lambda(hati - 3hatj + 2hatk)` and `vecr = 4hati + 5hatj + 6hatk + mu(2hati + 3hatj + hatk)`.

Find the shortest distance between the lines whose vector equations are `vecr = (1-t)hati + (t - 2)hatj + (3 -2t)hatk` and `vecr = (s+1)hati + (2s + 1)hatk`.

Find the shortest distance between lines `vecr = 6hati + 2hatj + 2hatk + lambda(hati - 2hatj + 2hatk)` and `vecr =-4hati - hatk + mu(3hati - 2hatj - 2hatk)`.

Find the unit vector in the direction of the vector `veca = hati + hatj + 2hatk`.

Find the unit vector in the direction of vector `vec(PQ)`, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

Integrate the function `(3x^2)/(x^6 + 1)`

Integrate the function `1/sqrt(1+4x^2)`

Integrate the function `1/sqrt((2-x)^2 + 1)`

Integrate the function `1/sqrt(9 - 25x^2)`

Integrate the function `(3x)/(1+ 2x^4)`

Integrate the function `x^2/(1 - x^6)`

Integrate the function `(x - 1)/sqrt(x^2 - 1)`

Integrate the function `x^2/sqrt(x^6 + a^6)`

Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`

Integrate the function `1/sqrt(x^2 +2x + 2)`

Integrate the function `1/(9x^2 + 6x + 5)`

Integrate the function `1/sqrt(7 - 6x - x^2)`