Three non-zero vectors satisfy A ⃗ \vec{A} A + B ⃗ \vec{B} B + C ⃗ \vec{C} C =0 with ∣ A ⃗ ∣ \left\vert\vec{A}\right\vert ​ A ​ =3, ∣ B ⃗ ∣ \left\vert\vec{B}\right\vert ​ B ​ =4 and ∣ C ⃗ ∣ \left\vert\vec{C}\right\vert ​ C ​ =5. Which set correctly gives A ⃗ \vec{A} A · B ⃗ \vec{B} B , | A ⃗ \vec{A} A x B ⃗ \vec{B} B |, the angle between A ⃗ \vec{A} A and B ⃗ \vec{B} B , and A ⃗ \vec{A} A ·( B ⃗ \vec{B} B × C ⃗ \vec{C} C )?

Physics · Mathematical tools and vector · Vectors

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Three non-zero vectors satisfy A⃗\vec{A}+B⃗\vec{B}+ C⃗\vec{C}=0 with ∣A⃗∣\left\vert\vec{A}\right\vert=3, ∣B⃗∣\left\vert\vec{B}\right\vert=4 and ∣C⃗∣\left\vert\vec{C}\right\vert=5. Which set correctly gives A⃗\vec{A}·B⃗\vec{B}, |A⃗\vec{A}xB⃗\vec{B}|, the angle between A⃗\vec{A} and B⃗\vec{B}, and A⃗\vec{A}·(B⃗\vec{B}×C⃗\vec{C})?

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