Question

Let the coordinates of a point P with respect to a system of non-coplanar vectors  be (3, 2, 1). Then, the coordinates of P with respect to the system of vectors  and 

Solution

Correct option is

(3/2, 1/2, 1)

 

Let the coordinates of P with respect to the new system be (xyz). Then,

      

                                                

  

Hence, the coordinates of P with respect to the new system are (3/2, 1/2, 1).  

 

SIMILAR QUESTIONS

Q2

 

If the position vector of the three points are ,

 then the three points are 

Q3

Three points with position vectors  will be collinear, if there exist scalars xyz such that   

Q4

The position vectors of the vertices ABC of a âˆ†ABC are  respectively. The length of the bisector AD of the angle BAC where D is on the line segment BC, is     

Q5

 

Consider points ABC and D with position vectors 

 respectively. Then, ABCD is a   

Q6

If the vectors  are the sides of a âˆ†ABC, then length of the median through A is 

Q7

The sides of a parallelogram are  then the unit vector parallel to one of the diagonals is 

Q8

If the points  are collinear, where  are three non-coplanar vectors, the value of t is 

Q9

A vector coplanar with vectors  and parallel to the vector  

Q10

 

If (xyz) ≠ (0, 0, 0) and  

 then the values of a are