If vec{A} times vec{B} = vec{B} times vec{A}, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The cross product of two vectors is anti-commutative,meaning $\vec{A} 	imes \vec{B} = -(\vec{B} 	imes \vec{A})$.Given the condition $\vec{A} 	i

Vedclass · Accepted Answer

$\pi$

Vedclass · Answer

(D) The cross product of two vectors is anti-commutative,meaning $\vec{A} 	imes \vec{B} = -(\vec{B} 	imes \vec{A})$.Given the condition $\vec{A} 	imes \vec{B} = \vec{B} 	imes \vec{A}$,we can substitute the anti-commutative property:$-(\vec{B} 	imes \vec{A}) = \vec{B} 	imes \vec{A}$.This implies $2(\vec{B} 	imes \vec{A}) = 0$,so $\vec{B} 	imes \vec{A} = 0$.The magnitude of the cross product is given by $|\vec{B} 	imes \vec{A}| = |B||A| \sin(	heta) = 0$.Since the vectors are non-zero,$\sin(	heta) = 0$,which means $	heta = 0$ or $	heta = \pi$.However,for the cross product to satisfy the equality $\vec{A} 	imes \vec{B} = \vec{B} 	imes \vec{A}$,both sides must be zero vectors. This occurs when the vectors are parallel $(	heta = 0)$ or anti-parallel $(	heta = \pi)$. Among the given options,$\pi$ is the correct choice.

If $\vec{A} \times \vec{B} = \vec{B} \times \vec{A}$,find the angle between $\vec{A}$ and $\vec{B}$.

Similar Questions

Given two vectors $\vec{A} = 3\hat{i} + \hat{j}$ and $\vec{B} = \hat{j} + 2\hat{k}$. Find the unit vector perpendicular to both $\vec{A}$ and $\vec{B}$.

Given two vectors $\vec{A} = 3\hat{i} + \hat{j}$ and $\vec{B} = \hat{j} + 2\hat{k}$. If these two vectors represent the adjacent sides of a parallelogram,find the area of the parallelogram.

Two vectors $\vec{A}$ and $\vec{B}$ are at right angles to each other,when

The area of the triangle formed by the vectors $\vec{a} = 2\hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = \hat{i} + \hat{j} + \hat{k}$ is:

$\overrightarrow A = 2\hat i + 4\hat j + 4\hat k$ and $\overrightarrow B = 4\hat i + 2\hat j - 4\hat k$ are two vectors. The angle between them will be ........ $^o$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module