Math, asked by prathibha15, 11 months ago

When will A cross B be equal to B cross A?​

Answers

Answered by Anonymous
12

vector product of two vectors is not commutative that is A cross B not equal to B cross A .

In this case magnitudes are equal but directions are opposite. It can be A cross B = -B cross A.

Answered by ushmagaur
3

Question: When will \vec A \times \vec B be equal to \vec B \times \vec A.

Answer:

\vec A \times \vec B = \vec B \times \vec A holds only when the angle between the vectors A and B is \pi.

Step-by-step explanation:

Cross product: The cross product or vector product is a binary operation on two vectors in a three-dimensional space.

Since the cross product is anti-commutative, i.e.,

\vec A \times \vec B=-\vec B \times \vec A

Given: \vec A \times \vec B=\vec B \times \vec A

We know that,

\vec A \times \vec B=ABsin\theta \hat{n} . . . . . (1)

where \theta is the angle between the vectors A and B.

Similarly,

\vec B \times \vec A=BAsin(2\pi -\theta) \hat{n} . . . . (2)

          =-BAsin\theta \hat n (Since sin(2\pi -\theta)=-sin\theta)

From (1) and (2), we have

sin(2\pi-\theta)=sin\theta

2\pi-\theta=\theta

2\pi=2\theta

\theta =\pi

Thus, the angle between the vectors A and B must be \pi.

Or, Vectors A and B must be in opposite direction.

#SPJ2

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