If $\vec{A} \times \vec{B}=\vec{B} \times \vec{A}$, then the angle between $A$ and $B$ is

JEE Main · 2004 · 24 Apr 2004 · Offline · Vector

A \times B = B \times A

, then the angle between

A

and

B

(A) $π$ ✓ Correct
(B) $π /3$
(C) $π /2$
(D) $π /4$

Answer: (A)

Solution

The vector product changes sign when the order of the factors is reversed,

A \times B = - B \times A

. For the product to stay the same on reversing the order, it must equal its own negative, which is only possible if it is the zero vector. That needs

sin θ = 0

, so the two vectors are either parallel or antiparallel; the condition is met when the angle between them is

18 0^{\circ}

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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