Question

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

Solution

Correct option is

 

Let A, B, C be the points with position vectors  respectively. These points will be collinear, if

              

  

  

  

SIMILAR QUESTIONS

Q1

If O and O denote respectively the circum-centre and orthocentre of∆ABC, then 

Q2

If O and O denote respectively the circum-centre and orthocenter of âˆ†ABC, then  

Q3

Consider âˆ†ABC and ∆A1B1C1 in such a way that  and M, N, M1, N1 be the mid-point of AB, BC, A1B1 and B1C1 respectively. Then,  

Q4

Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin, then  equals

Q5

If A, B, C, D be any four points and E and F be the middle points of AC and BD respectively, then  is equal to

Q6

Given that the vectors  are non-collinear, the values of x and yfor which the vector equality  holds true if  are  

Q7

Let  be three non-zero vectors, no two of which are collinear. If the vector  is collinear with  is collinear with  is equal to 

Q9

 

If the position vector of the three points are ,

 then the three points are 

Q10

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