Question

If A1 AND A2 ARE TWO NON COLLINEAR UNIT VECTOR. AND IF |A1+A2|=√3 THEN THE VALUE OF (A1-A2).(2A1-A2) IS.

Answer 1

Here is what you have to do If A1 AND A2 ARE TWO NON-COLLINEAR UNIT VECTOR. AND IF |A1+A2|=√3 THEN THE VALUE OF (A1-A2).(2A1-A2) IS.

|a1+a2|=√3

|a1+a2|2=3

(a1+a2).(a1+a2)=3

a1.a1+a2.a2+ 2a1.a2

|a1|2+|a2|2+2a1.a2=3

1+1+2a1.a2=3 (unit vectors)

a1.a2=1/2

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

=2|a1|2-|a2|2-a1.a2

=2-1-1/2=1/2

So the answer is ½

Answer 2

Answer:(a1 - a2). (2a1 +a2) is

(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

Explanation: