Home
Class 12
MATHS
Find the volume of the parallelepiped wh...

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors: ` vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j+2 hat k` ` vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j-2 hat k` ` vec a=11 hat i , vec b=2 hat j- hat k , vec c=13 hat k` ` vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k`

Text Solution

Verified by Experts

Volume of the parallelepiped can be given as triple product of three vectors.
(i)`V = [veca vecb vecc]`
`:. V = |[2,3,4],[1,2,-1],[3,-1,2]|`
`=>V = 2(3)-3(5)+4(-7)`
`=>V = -37`
But, volume can not be negative.
So, required volume is `37` cubic units.
...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SCALAR OR DOT PRODUCT

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

  • SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|82 Videos

Similar Questions

Explore conceptually related problems

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i+3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j+2hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i-3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j-2hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=hat i+hat j+hat k,vec b=hat i-hat j+hat k,vec c=hat i+2hat j-hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors vec(a)=2hat(i)-3hat(j)+hat(k),vec(b)=hat(i)-hat(j)+2hat(k) and vec(c)=2hat(i)+hat(j)-hat(k) .

Find the volume of the parallelepiped whose edges are represented by the vectors vec(a)=(2hat(i)-3hat(j)+4hat(k)), vec(b)=(hat(i)+2hat(j)-hat(k)) and vec(c)=(3hat(i)-hat(j)+2hat(k)) .

Show that each of the following triads of vectors are coplanar: vec a= hat i+2 hat j- hat k , vec b=3 hat i+2 hat j+7 hat k , vec c=5 hat i-6 hat j+5 hat k vec a=-4 hat i-6 hat j-2 hat k , vec b=- hat i+4 hat j+3 hat k , vec c=8 hat i- hat j+3 hat k hat a= hat i-2 hat j+3 hat k , vec b=-2 hat i+3 hat j-4 hat k , vec c= hat i-3 hat j+5 hat k

[vec a,vec b,vec c], when vec a=2hat i-3hat j+4hat k,vec b=hat i+2hat j-hat k and vec c=3hat i-hat j+2hat k

If vec a=3hat i-hat j-4hat k,vec b=2hat i+4hat j-3hat k and vec c=hat i+2hat j-widehat k, find |3vec a-2hat b+4hat c|

Find vec a.( vec bxx vec c)\ if\ vec a=2 hat i+ hat j+3 hat k ,\ vec b=- hat i+2 hat j+ hat k\ a n d\ vec c=3 hat i+ hat j+2 hat kdot

Find the area of the rriangle formed by the tips of the vectors, vec a= (2 hat I - hat j+ 3 hat k), vec b= 4 hat I + 3 hat j-hat k , vec C= 3 hat I - hat j + 2 hat k .

Home
Profile