vec{A},vec{B},and vec{C} are three non-collin | vedclass

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

Question

(A) The vector product $\vec{V} = \vec{B} 	imes \vec{C}$ results in a vector that is perpendicular to the plane containing $\vec{B}$ and $\vec{C}$.Ne

Vedclass · Accepted Answer

It is perpendicular to $\vec{A}$ and lies in the plane of $\vec{B}$ and $\vec{C}$.

Vedclass · Answer

(A) The vector product $\vec{V} = \vec{B} 	imes \vec{C}$ results in a vector that is perpendicular to the plane containing $\vec{B}$ and $\vec{C}$.Next,the vector product $\vec{A} 	imes \vec{V}$ results in a vector that is perpendicular to both $\vec{A}$ and $\vec{V}$.Since $\vec{V}$ is perpendicular to the plane of $\vec{B}$ and $\vec{C}$,any vector perpendicular to $\vec{V}$ must lie within the plane of $\vec{B}$ and $\vec{C}$.Therefore,$\vec{A} 	imes (\vec{B} 	imes \vec{C})$ lies in the plane of $\vec{B}$ and $\vec{C}$ and is perpendicular to $\vec{A}$.

$\vec{A}$,$\vec{B}$,and $\vec{C}$ are three non-collinear,non-coplanar vectors. What can you say about the direction of $\vec{A} \times (\vec{B} \times \vec{C})$?

Similar Questions

The resultant of two vectors having magnitudes $2$ and $3$ is $1$. What is their cross product?

If $|\overrightarrow{A}|=4$ unit,$|\overrightarrow{A}+\overrightarrow{B}|=10$ unit and $\overrightarrow{A} \cdot(\overrightarrow{A}+\overrightarrow{B})=20$ unit,then $|\overrightarrow{B}|=$ ?

Show that the area of the triangle formed by the vectors $\vec{a}$ and $\vec{b}$ is one-half of the magnitude of $\vec{a} \times \vec{b}$.

Show that $\vec{a} \cdot(\vec{b} \times \vec{c})$ is equal in magnitude to the volume of the parallelepiped formed by the three vectors $\vec{a}, \vec{b}$ and $\vec{c}$.

The two vectors $\vec A = -2\widehat i + \widehat j + 3\widehat k$ and $\vec B = 7\widehat i + 5\widehat j + 3\widehat k$ are :-

Vedclass Test Series

Exam Paper Generator

Online Exam Module