HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

If the vectors `3hat"i" + 5hat"k", 4hat"i" + 2hat"j" - 3hat"k"` and `3hat"i" + hat"j" + 4hat"k"`  are the coterminus edges of the parallelopiped, then find the volume of the parallelopiped.

If the vectors `- 3hati + 4hatj - 2hatk , hati + 2hatk` and `hati - phatj` are coplanar, then find the value of p.

If `bar"u" = hat"i" - 2hat"j" + hat"k" , bar"v" = 3hat"i" + hat"k"` and `bar"w" = hat"j" - hat"k"` are given vectors, then find `(bar"u" + bar"w").[(bar"u" xx bar"v") xx (bar"v" xx bar"w")]`

Using properties of scalar triple product, prove that `[(bara + barb,  barb + barc,  barc + bara)] = 2[(bara, barb, barc)]`.

Prove that the volume of a tetrahedron with coterminus edges `overlinea, overlineb` and `overlinec` is `1/6[(overlinea, overlineb, overlinec)]`.

Hence, find the volume of tetrahedron whose coterminus edges are `overlinea = hati + 2hatj + 3hatk, overlineb = -hati + hatj + 2hatk` and `overlinec = 2hati + hatj + 4hatk`.

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

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

If `2hati + 3hatj, hati + hatj + hatk` and `λhati + 4hatj + 2hatk` taken in order are coterminous edges of a parallelopiped of volume 2 cu. units, then find the value of λ.

Find the volume of the parallelopiped whose coterminous edges are `2hati - 3hatj, hati + hatj - hatk` and `3hati - hatk`.

If `bar"u" = hat"i" - 2hat"j" + hat"k" , bar"v" = 3hat"i" + hat"k"` and `bar"w" = hat"j" - hat"k"` are given vectors, then find `[bar"u" xx bar"v"     bar"u" xx bar"w"     bar"v" xx bar"w"]`

If the points A(1, 2, 3), B(–1, 1, 2), C(2, 3, 4) and D(–1, x, 0) are coplanar find the value of x.

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`

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

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

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

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

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

If `u=hati -2hatj + hatk, barr=3hati + hatk and w=hatj, hatk`  are given vectors, then find `[baru + barw]. [(barw xx barr)xx(barr xx barw)]`