Question

For three vectors  which of the following expressions is not equal to any of the remaining three?

Solution

Correct option is

 

We have,   

      

So, expression in options (i) and (ii) are equal.   

Since the positions of dot and cross can be interchanged in scalar triple product. Therefore,   

       

So, expression in options (i) and (iv) are equal.

  

Hence, expression in (iii) is note equal to the remaining three.

SIMILAR QUESTIONS

Q1

The three concurrent edges of a parallelopiped represent the vectors  such that  Then, the volume of the parallelopiped whose three concurrent edges are the three diagonals of three faces of the given parallelepiped is    

Q2

Which of the following expressions are meaningful?

Q3

 are linearly dependent vectors and , then

Q4

The volume of the tetrahedron whose vertices are the points with position vectors  and  is 11 cubic units if the value of λ is 

Q5

If a vector  is expressed as the sum of two vectors  along and perpendicular to a given vector 

Q6

 are two given vectors. On these vectors as adjacent sides a parallelogram is constructed. The vector which is the altitude of the parallelogram and which is perpendicular to  is not equal to

Q7

Let  be a unit vector and  a non-zero vector not parallel to . The angles of the triangle, two of whose sides are represented by  

Q8

Three vectors  taken two at a time form three planes. The three unit vectors drawn perpendicular to three planes form a parallelopiped of volume