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Vector Algebra question

2004 · Shift 0 · Q185

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JEE Main
Physics
Vector Algebra
2004 · Shift 0 · Q185

Vector Algebra question

2004 · Shift 0 · Q185

JEE MainPhysicsVector AlgebraMCQ+4 / −1

If

\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A

, then the angle beetween A and B is

A
${\pi \over 2}$
B
${\pi \over 3}$
C
$\pi$
D
${\pi \over 4}$

View written solutionFree

Correct answer: C

Use the anti-commutative property of cross product:

$\vec A \times \vec B = -\,(\vec B \times \vec A)$

But the question gives:

$\vec A \times \vec B = \vec B \times \vec A$

Combine both relations.

Since

$\vec A \times \vec B = -\,(\vec B \times \vec A)$

and also

$\vec A \times \vec B = \vec B \times \vec A,$

we get

$\vec A \times \vec B = -\,(\vec A \times \vec B)$

So,

$2(\vec A \times \vec B)=0$

which implies

$\vec A \times \vec B=0$

Condition for zero cross product:

$|\vec A \times \vec B| = AB\sin\theta = 0$

Thus,

$\sin\theta = 0$

So possible angles are

$\theta = 0 \text{ or } \pi$

Check the options.

Given options are:

$\dfrac{\pi}{2}$
$\dfrac{\pi}{3}$
$\pi$
$\dfrac{\pi}{4}$

Among these, only $\pi$ is present.

Therefore, the correct option is:

$\boxed{\pi}$

So, Option C is correct.

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