Question

 

If (xyz) ≠ (0, 0, 0) and  

 then the values of a are

Solution

Correct option is

0, –1

 

The given vector equation can be written as

  

 are linearly independent vectors.   

       x – (3 + a)y + 5z = 0  

       3x + y – az = 0   

Eliminating xyz, we get   

     

SIMILAR QUESTIONS

Q1

 

If the position vector of the three points are ,

 then the three points are 

Q2

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

Q3

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     

Q4

 

Consider points ABC and D with position vectors 

 respectively. Then, ABCD is a   

Q5

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

Q6

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

Q7

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

Q8

A vector coplanar with vectors  and parallel to the vector  

Q9

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 

Q10

The vector  lies in the plane of the vectors  bisects the angle between . Then , which one of the following gives the possible values of α and β?