We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more   

AtoZmath.com
Support us
(New) All problem can be solved using search box
I want to sell my website www.AtoZmath.com with complete code
Home What's new College Algebra Games Feedback About us
Algebra Matrix & Vector Numerical Methods Statistical Methods Operation Research Word Problems Calculus Geometry Pre-Algebra


Home > Matrix & Vector calculators > Volume of Parallelepiped determined by vectors example
19. Volume of Parallelepiped determined by vectors example ( Enter your problem )
( Enter your problem )
  1. Example-1
  2. Example-2
 		Other related methods
  1. Addition/Subtraction of two vectors
  2. Scalar Multiplication of vectors
  3. Dot Product of two vectors
  4. Cross Product of two vectors
  5. Magnitude(length) of a vector
  6. Unit vector
  7. Direction cosines of a vector
  8. Component form of a vector given two points
  9. Angle between two vectors
  10. Vector projections of b onto a
  11. Orthogonal vectors
  12. Collinear vectors
  13. Coplanar vectors
  14. Scalar triple product
  15. Vector triple product
  16. Area of triangle determined by two vectors
  17. Area of parallelogram determined by two vectors
  18. Volume of pyramid determined by vectors
  19. Volume of Parallelepiped determined by vectors
  20. Decomposition of vector in basis
  21. Linearly dependent and linearly independent vectors
1. Example-1
(Previous example)		20. Decomposition of vector in basis
(Next method)

2. Example-2


1. Find VolumeParallelepiped(A,B,C)
`A=(5,6,1)`,`B=(0,2,3)`,`C=(3,4,5)`

Solution:
Here `vec A=(5,6,1),vec B=(0,2,3),vec C=(3,4,5)`


Volume `=|vec C * (vec A xx vec B)|`

1. Calculate scalar triple product
`C*(A xx B)`

`=|[C_1,C_2,C_3],[A_1,A_2,A_3],[B_1,B_2,B_3]|`

`=|[3,4,5],[5,6,1],[0,2,3]|`

`=3(6xx3-1xx2)-4(5xx3-1xx0)+5(5xx2-6xx0)`

`=3(18-2)-4(15-0)+5(10-0)`

`=3(16)-4(15)+5(10)`

`=48-60+50`

`=38`

2. Calculate parallelepiped volume
Volume `=38`
2. Find VOLUMEPARALLELEPIPED(A,B,C)
`A=(0,2,3)`,`B=(5,6,1)`,`C=(1,5,6)`

Solution:
Here `vec A=(0,2,3),vec B=(5,6,1),vec C=(1,5,6)`


Volume `=|vec C * (vec A xx vec B)|`

1. Calculate scalar triple product
`C*(A xx B)`

`=|[C_1,C_2,C_3],[A_1,A_2,A_3],[B_1,B_2,B_3]|`

`=|[1,5,6],[0,2,3],[5,6,1]|`

`=1(2xx1-3xx6)-5(0xx1-3xx5)+6(0xx6-2xx5)`

`=1(2-18)-5(0-15)+6(0-10)`

`=1(-16)-5(-15)+6(-10)`

`=-16+75-60`

`=-1`

2. Calculate parallelepiped volume
Volume `=1`

This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here


1. Example-1
(Previous example)		20. Decomposition of vector in basis
(Next method)


Share this solution or page with your friends.


Home What's new College Algebra Games Feedback About us
 
Copyright © 2024. All rights reserved. Terms, Privacy
 
 

.