PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

The plane 2x − (1 + λ) y + 3λz = 0 passes through the intersection of the planes

The equation of the plane through the intersection of the planes x + 2y + 3z = 4 and 2x + y − z = −5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 is

The equation of the plane through the line x + y + z + 3 = 0 = 2x − y + 3z + 1 and parallel to the line \[\frac{x}{1} = \frac{y}{2} = \frac{z}{3}\] is 

A plane meets the coordinate axes at A, B and C such that the centroid of ∆ABC is the point (a, b, c). If the equation of the plane is \[\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = k,\] then k = 

A vector parallel to the line of intersection of the planes\[\vec{r} \cdot \left( 3 \hat{i} - \hat{j} + \hat{k}  \right) = 1 \text{ and }  \vec{r} \cdot \left( \hat{i} + 4 \hat{j}  - 2 \hat{k}  \right) = 2\] is 

The distance of the point (−1, −5, −10) from the point of intersection of the line \[\vec{r} = 2 \hat{i}- \hat{j} + 2 \hat{k}  + \lambda\left( 3 \hat{i}  + 4 \hat{j}+ 12 \hat{k}  \right)\]   and the plane \[\vec{r} \cdot \left( \hat{i} - \hat{j} + \hat{k}  \right) = 5\] is 

The equation of the plane through the intersection of the planes ax + by + cz + d = 0 andlx + my + nz + p = 0 and parallel to the line y=0, z=0

The equation of the plane which cuts equal intercepts of unit length on the coordinate axes is

Solve the following matrix equation for x: `[x 1] [[1,0],[−2,0]]=0`

If A =  `([cos alpha, sin alpha],[-sinalpha, cos alpha])` , find α satisfying 0 < α < `pi/r`when `A+A^T=sqrt2I_2` where A^T is transpose of A.

If `A=([2,0,1],[2,1,3],[1,-1,0])` find A² - 5A + 4I and hence find a matrix X such that  A² - 5A + 4I + X = 0

If `veca and vecb` are perpendicular vectors, `|veca+vecb| = 13 and |veca| = 5` ,find the value of `|vecb|.`

Compute the following sums:

`[[3   -2],[1           4]]+ [[-2         4 ],[1           3]]`

Compute the following sums:

`[[2    1   3],[0   3   5],[-1   2   5]]`+ `[[1 -2     3],[2            6        1],[0   -3       1]]`

Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`and `c =[[-2,5],[3,4]]`.Find each of the following: 2A − 3B

Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`and `c =[[-2,5],[3,4]]`.Find each of the following:  B − 4C

Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`and `c =[[-2,5],[3,4]]`.Find each of the following: 3A − C

Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`and `c =[[-2,5],[3,4]]`.Find each of the following: 3A − 2B + 3C

If A =`[[2,3],[5,7]],B =` `[[-1,0 ,2],[3,4,1]]`,`C= [[-1,2,3],[2,1,0]]`find : A + B and B + C

If A =`[[2   3],[5   7]],B =` `[[-1   0   2],[3    4      1]]`,`C= [[-1    2   3],[2    1     0]]`find

2B + 3A and 3C − 4B