Question

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

Solution

Correct option is

 

  

∴ Required volume 

     

     

     

Now,

     

And,

          

         

  

  

Hence, required volume 

SIMILAR QUESTIONS

Q1

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

Q2

 are linearly dependent vectors and , then

Q3

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

Q4

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

Q5

 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

Q6

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  

Q7

 If  is a vector such that  and the angle between  is 30o, then  

Q8

Let  be two non-collinear unit vectors. If 

Q9

If the vectors  are coplanar, then the value of pqr – (p + q + r) is 

Q10

If  are any three vectors such that