Question

If the sum of two unit vectors is a unit vector, then the magnitude of their difference, is

Solution

Correct option is

 

Let  be two unit vectors represented by sides OA and AB of a triangle OAB. Then,  and  

                      

 

It is given that   

            

⇒      OA = AB = OB = 1   

⇒  âˆ†OAB is an equilateral triangle

∴   âˆ†OAB’ is an isosceles triangle 

  

  

In ∆BOB’, we have   

         

  

.

SIMILAR QUESTIONS

Q1

If ABCD is a rhombus whose diagonals cut at the origin O, then  equals

Q2

If C is the midpoint of AB and P is any point outside AB, then  

Q3

The non-zero vectors  are related by . Then the angle between 

Q4

If ABCDEF is a regular hexagon with 

Q5

If  are the position vectors of A, B respectively and C is a point on AB produced such that AC = 3 AB, then the position vector of C is 

Q6

Let  be the angle bisector of A of ∆ABC such that  then

Q7

Let D, E, F be the middle points of the sides BC, CA, AB respectively of a triangle ABC. Then,  equals

Q8

If G is the centroid of a triangle ABC, then  equals 

Q9

Let ABC be a triangle having its centroid at G. If S is any point in the plane of the triangle, then 

Q10

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