Grade 11Mechanics
Given |Ā1| = 2 , |Ā2|=3 and |Ā1+Ā2| = 3 . The magnitude of (Ā1+2Ā2).(3Ā1 - 4Ā2) is ?
1 Answer
Vikas TU
|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
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