Question

if a1 bar and a2 two non collinear unit vectors inclined at 60 degrees with each other then the value of (a1 bar-a2 bar). 2a1 bar+2a2 bar)

Answer 1

Explanation:

(a1 + a2) = √a1² + a2² + 2a1a2cosΦ

√3 = √1+1+2cosΦ

√3 = 2cosΦ/2

CosΦ/2 = √3/2

Φ/2 = 30°

Φ = 60°

(a1-a2) . (2a1+ a2)

2a²-(a1 . a2)+2(a1.a2)-2a2² = 0

2+a1a2cosΦ-2 = 0

2+cosΦ-2 = 0

CosΦ = 0

Cos 60° = 1/2.

Answer is 1/2

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