Two vectors, a and b, are unit vectors with an angle of 60 degrees between them

pedzenekO

pedzenekO

Answered question

2021-08-19

Two vectors, a and b, are unit vectors with an angle of 60 degrees between them (when tail-to-tail).
If the vectors below are orthogonal, what is the value(s) of m?
u= a-3b
v=ma + b

Answer & Explanation

SabadisO

SabadisO

Skilled2021-08-20Added 108 answers

Given:
The vectors u=a3b and v=ma+b are orthogonal.
The vectors a and b are unit vectors with an angle of 60 degrees between them.
As u and v are orthogonal vectors, therefore, u·v=0.
(a3b)(ma+b)=a(ma+b)3b(ma+b)=
=ma2+ab3mba3b2
As a and b are unit vectors, therefore, |a|=1, |b|=1
As ab=|a||b|cosθ
(a3b)(ma+b)=m(1)+|a||b|cos(60)3m|b||a|cos(60)3(1)=m+(1)(1)(12)3m(1)(1)(12)3=m+123m23
Therefore,
uv=m252=0
Simplifying the above equation,
m252=0
m2=52
Multiply both sides by 2,
-m=5
m=-5

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