HSC Arts (Marathi Medium) 12th Standard Board Exam [इयत्ता १२ वी] - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

In the triangle `PQR, bar (PQ) = 2bara and bar (QR) = 2barb`. The mid-point of PR is M. Find following vectors in terms of `bar a and bar b`.

1. `bar(PR)`
2. `bar(PM)`
3. `bar(QM)`

If a vector has direction angles 45ºand 60º find the third direction angle. 

The position vector of points A and B are `6 bar "a" + 2 bar "b" and bar "a" - 3 bar"b"`. If the point C divided AB in the ratio 3 : 2, show that the position vector of C is `3 bar "a" - bar "b".`

The position vector of points A and B are `6bara +2barb ` and `bara-3barb `.If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is `3bara-barb` .

The position vector of points A and B are `6bara + 2 barb and bara - 3 barb`. If point C divides AB in the ratio 3 : 2, then show that the position vector of C is `3bara - barb`.

The position vector of points A and B are `6bara + 2 barb and bara - 3 barb`. If point C divides AB in the ratio 3 : 2, then show that the position vector of C is `3bara - barb`.

The position vector of points A and B are `6bara + 2 barb` and `bara-3 barb`. If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is `3bara -barb`.

The position vector of points A and B are `6 bara + 2barb and bara - 3barb.` If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is `3bara - barb.`

Determine whether `bara " and"  barb`  are orthogonal, parallel or neither.

`bara=-3/5hati +1/2hatj +1/3hatk, barb= 5hati+4hatj+3hatk `

Determine whether `bara and bar b` are orthogonal, parallel or neither.

`bar"a" = -3/5hat"i" + 1/2hat"j" + 1/3hat"k" , barb = 5hat"i" + 4hat"j" + 3hat"k"`

Find the angle between the line `bar r = (hat i + 2hat j + hat k) + lambda(hat i + hat j + hat k)` and the plane `bar r *(2hat i + hat j + hat k) = 8`.

Find two unit vectors each of which is perpendicular to both `baru` and `barv`, where `baru = 2hati + hatj - 2hatk, barv = hati +  2hatj - 2hatk`

Determine whether `bb(bara)` and `bb(barb)` are orthogonal, parallel, or neither.

`bara = -3/5 hati + 1/2 hatj +1/3 hatk,  barb = 5 hati + 4 hatj + 3 hatk`

If a vector has direction angles 45° and 60° find the third direction angle.

If a vector has direction angles 45º and 60º, find the third direction angle.

If a vector has direction angles 45º and 60º find the third direction angle.

If a vector has direction angles 45ºand 60º find the third direction angle.

Find two unit vectors each of which is perpendicular to both `baru` and `barv`, where `baru = 2hati + hatj - 2hatk, barv = hati + 2hatj - 2hatk`.

Determine whether `bara and barb` and are orthogonal, parallel or neither.

`bara = -3/5hati + 1/2hatj + 1/3hatk,  barb = 5hati + 4hatj + 3hatk`

Find two unit vectors each of which is perpendicular to both `baru and barv, "where"  baru = 2hati + hatj - 2hatk , barv = hati + 2hatj - 2hatk`