Question

Given |A1| and |A2|=3 and |A1+A2|=3
Find the value of (A1, +Ā2). (3Ā - 4A)​

Answer 1

Answer:

|A1 + A2|^2 = |A1|^2 + |A2|^2 + 2A1.A2.cosα

32 = 22 + 32 + 2x2x3 cosα

cos α = -4/12

cosα = -1/3

(Ā1+2Ā2).(3Ā1 - 4Ā2)

= 3|Ā1|2 - 4 Ā2||Ā1| cosα + 6|Ā2||Ā1|cosα- 8|Ā2|2

= 3x4 – 4x 3x 2x(-1)/3 + 6x3x2x(-1)/3- 8x9

= 12 +8 -12-72

= 20 – 84

= -64

Magnitude is 64