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

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

Find two unit vectors each of which is perpendicular to both

`baru  "and"  barv, "where"  baru = 2hati + hatj - 2hatk,  barv = hati + 2hatj - 2hatk`

Find two unit vectors each of which is perpendicular to both `\overline "u" and \overline "v",` where ` \overline "u" = 2hati + hatj - 2hatk, \overline "v" = hati + 2hatj - 2hatk`

If a vector has direction angles 45º and 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`

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

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

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

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

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

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` are orthogonal, parallel or neither.

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

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

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

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

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

Find the volume of the parallelopiped whose vertices are A (3, 2, −1), B (−2, 2, −3) C (3, 5, −2) and D (−2, 5, 4). 

If `barc = 3bara - 2barb` and `[bara     barb + barc     bara + barb + barc]` = 0 then prove that `[bara  barb  barc]` = 0

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

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

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

`"If"  barc=3bara-2barb   "and" [bara    barb+barc     bara+barb+barc]= 0  "then prove that" [bara  barb  barc]=0  `

If `barc= 3bara - 2barb  and [bara  barb+barc  bara+barb+barc] = "then proved" [bara barb barc] = 0`