WORKSHEET 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 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

Problem 6 :

Determine whether the three vectors

are coplanar.

Solution

Problem 7 :

Let 

If c₁ = 1 and c₂ = 2, find c₃ such that 

are coplanar.

Solution

Problem 8 :

If 

show that 

depends on neither x nor y.

Solution

Problem 9 :

If the vectors 

are coplanar, prove that c is the geometric mean of a and b.

Solution

Problem 10 :

Let

the three non zero vectors such that c vector is a unit perpendicular to both a vector and c vector. If the angle between a vector and b vector is π/6, show that

Solution