PROBLEMS ON SCALAR TRIPLE PRODUCT

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 :

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