If  are Three Non-coplanar, Non-zero Vectors, Then              is Equal To 

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Question

 

If  are three non-coplanar, non-zero vectors, then

             is equal to 

Solution

Correct option is

 

Since  are non-coplanar vectors. Therefore, so are the vectors   

We know that any vector in space is expressible as the linear combination of three non-coplanar vectors. So, let   

      

Taking dot products successively with  we get   

     

Substituting these values in (i), we obtain that the given expression is equal to    

SIMILAR QUESTIONS

Q1

Let  be two non-collinear unit vectors. If 

Q2

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

Q3

If  are any three vectors such that 

Q4

Let  the value of λ for which the vector  is parallel to the plane containing  

Q5

Let  be three unit vectors such that  If the angle between , then the volume of the parallelepiped whose three conterminus edges are  

Q6

If the acute angle that the vector  makes with the plane of the two vectors  is , then 

Q7

 

If  are non-coplanar vectors and  are reciprocal vectors, then   

    

Q8

If  are non-zero and non-collinear vectors, then is equal to

Q9

 

If  is a unit vector such that   

       

 is equal to 

Q10

Let  be three vectors such that  If  be perpendicular to , then the value of l + m + n is