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

Prove that the volume of a parallelopiped with coterminal edges as  ` bara ,bar b , barc `

Hence find the volume of the parallelopiped with coterminal edges  `bar i+barj, barj+bark `

If `bar c = 3bara- 2bar b ` Prove that `[bar a bar b barc]=0`

Show that the four points A(4, 5, 1), B(0, –1, –1), C(3, 9, 4) and D(–4, 4, 4) are coplanar.

Find λ, if the vectors `veca=hati+3hatj+hatk,vecb=2hati−hatj−hatk and vecc=λhatj+3hatk`  are coplanar.

Find the volume of the parallelopiped whose coterminus edges are given by vectors

`2hati+3hatj-4hatk, 5hati+7hatj+5hatk and 4hati+5hatj-2hatk`

If `bara=3hati-hatj+4hatk, barb=2hati+3hatj-hatk, barc=-5hati+2hatj+3hatk` then `bara.(barbxxbarc)=`

(A) 100

(B) 101

(C) 110

(D) 109

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

if `bara = 3hati - 2hatj+7hatk`, `barb  = 5hati + hatj -2hatk`and `barc = hati + hatj - hatk` then find `bara.(barbxxbarc)`

Find the volume of the parallelopiped whose coterminus edges are given by vectors `2hati+5hatj-4hatk, 5hati+7hatj+5hatk and 4hati+5hatj-2hatk`

Find the volume of the parallelopiped, if the coterminus edges are given by the vectors `2hat"i" + 5hat"j" -4 hat"k", 5hat"i" +7hat"j"+5 hat "k" , 4hat"i" +5hat"j" - 2 hat"k"`.                               

Find the value of p, if the vectors `hat"i" - 2hat"j" + hat"k", 2hat"i" -5hat"j"+"p" hat "k" , 5hat"i" -9hat"j" + 4 hat"k"` are coplanar.

Determine where `bar"a"` and `bar"b"` are orthogonal, parallel or neithe:

`bar"a" = - 9hat"i" + 6hat"j" + 15hat"k"` , `bar"b" = 6hat"i" - 4hat"j" - 10hat"k"`.

Determine where `bar"a"` and `bar"b"` are orthogonal, parallel or neithe:

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

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

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

Determine where `bar"a"` and `bar"b"` are orthogonal, parallel or neithe:

`bar"a" = 4hat"i" - hat"j" + 6hat"k"` , `bar"b" = 5hat"i" - 2hat"j" + 4hat"k"`

Prove by vector method, that the angle subtended on semicircle is a right angle.

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

If a line has the direction ratios 4, −12, 18, then find its direction cosines

Find the angle between the lines whose direction cosines l, m, n satisfy the equations 5l + m + 3n = 0 and 5mn − 2nl + 6lm = 0.

Find `bar"a".(bar"b" xx bar"c")` if `bar"a" = 3hat"i" - hat"j" + 4hat"k" , bar"b" = 2hat"i" + 3hat"j" - hat"k"` and `bar"c" = - 5hat"i" + 2hat"j" + 3hat"k"`