For a given set of three vectors
the scalar
is called a scalar triple product of
If
Volume of parallelopiped :
The absolute value of a scalar triple product represents the volume of a box (rectangular parallelepiped), a scalar triple product is also called a box product.
What is coplanar ?
The scalar triple product of three non-zero vectors is zero if, and only if, the three vectors are coplanar.
Problem 1 :
If
find
Solution :
Problem 2 :
Find the volume of the parallelepiped whose coterminous edges are represented by the vectors
Solution :
Problem 3 :
The volume of the parallelepiped whose coterminus edges are
is 90 cubic units. Find the value of 𝜆.
Solution :
Problem 4 :
If
are three non-coplanar vectors represented by concurrent edges of a parallelepiped of volume 4 cubic units, find the value of
Solution :
Problem 5 :
Find the altitude of a parallelepiped determined by the vectors
if the base is taken as a parallelogram determined by
Solution :
Volume of 3D shape = base area x height
Base will be in the shape of parallelogram created by the vectors,
Base area of parallelogram :
Finding height :
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM