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If \(\vec{D} = (\vec{B} \times \vec{C})\), then \(\vec{D}\) is __________

Question and options

If D⃗=(B⃗×C⃗)\vec{D} = (\vec{B} \times \vec{C}), then D⃗\vec{D} is __________
  1. parallel to B⃗\vec{B}
  2. parallel to C⃗\vec{C}
  3. perpendicular to both B⃗\vec{B} and C⃗\vec{C}
  4. at 45° to both B⃗\vec{B} and C⃗\vec{C}

Answer and explanation

Correct answer: C - perpendicular to both \(\vec{B}\) and \(\vec{C}\)
D⃗=B⃗×C⃗\vec{D} = \vec{B} \times \vec{C}; a cross product is perpendicular to the plane containing B⃗\vec{B} and C⃗\vec{C}, so D⃗\vec{D} is perpendicular to both (not parallel to either, nor at 45∘45^\circ).

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