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Grade: 11

                        

if the sum of 2 unit vectors is also a unit vector, then the magnitude of their difference and angle between the 2 given vectors is

3 years ago

Answers : (2)

Ayush kumar
34 Points
							

Let ai+bj and ci+dj be the unit vectors.
From the defination,
a2+b2=1
(a2+b2)=1___(1)
c2+d2=1
(c2+d2)=1
____(2)

Add the above two vectors,
(ai+bj)+(ci+dj) =(a+c)i+(b+d)j__(3)

Also given that,
The magnitude of equation(3) is also unity.
(a+c)2+(b+d)2=1
((a+c)2+(b+d)2)=1
(a2+c2+2ac)+(b2+d2+2bd)=1
1+2ac+1+2bd=1
1+2ac+2bd+1=1
ac+bd=12___(4)
the magnitude of their difference is:?
THe difference of two unit vectors is 
(ai+bj)(ci+dj)=(ac)i+(bd)j
Magnitude=(ac)2+(bd)2
=a2+c22ac+b2+d22bd
=1+12(ac+bd) [From (1) and (2)]
=22(12) [From equation(4)

=2+1
=3
=1.73205

 

3 years ago
Arun
24742 Points
							
 

let two vectors are a,b then

 

resultant of sum = (a2 + b2 + 2abcos@)1/2 = 1               (given)

 

a = b = 1          (unit vector)

 

 1+1+2cos@ = 1

 

      cos@ = -1/2           .................1

 

now resultant of difference = magnitude (a-b)

 

R = (a2 + b2 - 2abcos@)1/2

 

a = b = 1 , cos@ = -1/2 so

 

R = [ 1+1+1]1/2 = root3

3 years ago
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