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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

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3 years ago

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)=(a−c)i+(b−d)jMagnitude=√(a−c)2+(b−d)2=√a2+c2−2ac+b2+d2−2bd=√1+1−2(ac+bd) [From (1) and (2)]=√2−2(−12) [From equation(4)=√2+1=√3=1.73205
```
3 years ago
Arun
25768 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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### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions