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If a b c are unit vectors such that a is perpendicular to plane BC and angle between BC is 60° then find |a + b + c|

If a b c are unit vectors such that a is perpendicular to plane BC and angle between BC is 60° then find |a + b + c|

Grade:11

2 Answers

Aastha Singh
askIITians Faculty 212 Points
3 years ago
DEAR STUDENT,
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Isha
13 Points
one year ago
a is perpendicular to the plane of b and c. 
Thus
a. b=0
a. c=0
Now, angle between b and c is 60
Thus, b. c =|b||c|cos60 =1.1.1/2
b. c=1/2
Hence
|a+b+c|^2 =|a|^2 +|b|^2 +|c|^2 +2(a.b+b.c+c.a) 
                  =1+1+1+2(0+1/2+0) 
                  =3+2×1/2 =4
Therefore   |a+b+c|=2

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