Let a and b be two vectors such that |a |=1 , |b |=4 and a b=2. If c= (2a b )-3b and the angle between b and c is , then 192 sin^2 ⁡ is equal to_____

Question

Accepted Answer

Correct answer: 48. (48) b c= (2a b ) b-3 |b |^2 |b | |c | cos ⁡ =-3 |b |^2 |c | cos ⁡ =-12 , as |b |=4a b=2 cos ⁡ = 12 ⇒ = 3 |c |^2= | (2a b )-3b |^2=64 34+144=192 |c |^2 cos^2 ⁡ =144192 cos^2 ⁡ =144192 sin^2 ⁡ =48

$Let a and b be two vectors such that | a | = 1, | b | = 4 and a \cdot b = 2 . If c = (2 a \times b) - 3 b and the angle between b and c is α, then 192 sin^{2} α is equal to_____$

Solution

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