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

Show that the vectors `2hati - 3hatj + 4hatk` and `-4hati + 6hatj -  8hatk` are collinear.

Evaluate the product `(3veca - 5vecb).(2veca + 7vecb)`.

Find `|vecx|`, if for a unit vector veca , `(vecx -  veca).(vecx + veca) = 12`.

If  `veca.veca = 0` and `veca . vecb = 0,` then what can be concluded about the vector `vecb`?

If either vector `veca = vec0`  or `vecb = vec0`, then `veca.vecb = 0`. But the converse need not be true. Justify your answer with an example.

Show that the vectors `2hati - hatj + hatk, hati - 3hatj - 5hatk`  and `3hati - 4hatj - 4hatk` from the vertices of a right angled triangle.

Show that the points A, B, C with position vectors `2hati- hatj + hatk`, `hati - 3hatj - 5hatk` and `3hati - 4hatj - 4hatk` respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle

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

Let A = `[[-1    0    2],[3     1      4]]``B=[[0      -2     5],[1      -3     1]]``and C = [[1     -5       2],[6     0    -4 ]]`Compute2A2-3B +4C : 

If A = diag (2 − 59), B = diag (11 − 4) and C = diag (−6 3 4), find

B + C − 2A

If A = diag (2 − 59), B = diag (11 − 4) and C = diag (−6 3 4), find

2A + 3B − 5C

Find matrices X and Y, if X + Y =`[[5     2],[0       9]]`

and X − Y =  `[[3       6],[0   -1]]`

Find X if Y =`[[3       2],[1      4]]`and 2X + Y =`[[1       0],[-3        2]]`