If veca is perpendicular to b and c,|a|=2, |b|=3|c|=4 and the angle between b and c is (2π /3), then [abc] is equal to:

Question

If veca is perpendicular to b and c,|a|=2, |b|=3|c|=4 and the angle between b and c is (2π /3), then [abc] is equal to: (A)  4√3  (B)  6√3  (C)  12√3  (D)  18√3

Tardigrade Admin · Accepted Answer

∵ [a b c]=a.(b× c) =a.( |b|c| sin (2π /3) hatn ) =|a|.|b||c|( sin (2π /3) )=2× 3× 4× (√3/2) =12√3

Q. If $a$ is perpendicular to $b$ and $c, ∣ a ∣ = 2,$ $∣ b ∣ = 3∣ c ∣ = 4$ and the angle between $b$ and $c$ is $\frac{2 π}{3},$ then $[a b c]$ is equal to:

$43$

$63$

$123$

$183$

$83$

$∵$ $[a b c] = a . (b \times c)$
$= a . (∣ b ∣ c ∣ sin \frac{2 π}{3} \overset{n}{^})$
$= ∣ a ∣.∣ b ∣∣ c ∣ (sin \frac{2 π}{3}) = 2 \times 3 \times 4 \times \frac{3}{2}$
$= 123$

Q. If a is perpendicular to b and c,∣a∣=2, ∣b∣=3∣c∣=4 and the angle between b and c is 32π​, then [abc] is equal to:

43​

63​

123​

183​

83​

∵ [abc]=a.(b×c) =a.(∣b∣c∣sin32π​n^) =∣a∣.∣b∣∣c∣(sin32π​)=2×3×4×23​​ =123​