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sum of two unit vector is also a unit vector then maganitude of their difference is

sum of two unit vector is also a  unit vector then maganitude of their difference is

Grade:11

2 Answers

Priyanshu Gujjar
94 Points
2 years ago

a+b∣=1

∣a∣2+∣b∣2+2∣a∣∣b∣cosθ​=1
→2(1+cosθ)=1
→cosθ=2−1​θ=120∘
∣a+b∣=∣a∣+∣b∣2−2∣a∣∣b∣cosθ​
=1+1−2cos120∘​
=2+2×21​​=3​.
Heer Shah
19 Points
2 years ago
let a,b be two unit vector at angle q
And c be there resultant unit vector.
Thus 1=a²+b²+2abcos(q)
1=1+1+2.1.1.cos(q)
cosq= -1/2
q=2pi/3
 
|a-b|=root(a²+b²+2ab cos(pi-2pi/3)
(Pi-2pi/3) because direction of b is reverse and we are adding (-b) to A vector.
|a-b|=root(1+1+2×1/2)=root(3)

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