PROBLEMS ON SCALAR TRIPLE PRODUCT

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 parallelopiped 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 parallelopiped of volume 4 cubic units, find the value of

Solution :

Problem 5 :

Find the altitude of a parallelopiped 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 :

Problem 6 :

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors

Solution :

Problem 7 :

Find the volume of the parallelopiped whose coterminous edges are represented by the vectors

Solution :

Problem 8 :

The volume of the parallelopiped whose coterminus edges are

is 90 cubic units. Find the value of 𝜆.

Solution :

Problem 9 :

If 

are three non-coplanar vectors represented by concurrent edges of a parallelepiped of volume 4 cubic units, find the value of

Solution :

Problem 10 :

Find the altitude of a parallelopiped 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 :