If a(vec{alpha} times vec{beta}) + b(vec{beta | vedclass

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

Question

(C) Given the equation $a(\vec{\alpha} 	imes \vec{\beta}) + b(\vec{\beta} 	imes \vec{\gamma}) + c(\vec{\gamma} 	imes \vec{\alpha}) = \overrightarro

Vedclass · Accepted Answer

coplanar

Vedclass · Answer

(C) Given the equation $a(\vec{\alpha} 	imes \vec{\beta}) + b(\vec{\beta} 	imes \vec{\gamma}) + c(\vec{\gamma} 	imes \vec{\alpha}) = \overrightarrow{0}$.Let $\vec{u} = \vec{\alpha} 	imes \vec{\beta}$,$\vec{v} = \vec{\beta} 	imes \vec{\gamma}$,and $\vec{w} = \vec{\gamma} 	imes \vec{\alpha}$.The given equation is $a\vec{u} + b\vec{v} + c\vec{w} = \overrightarrow{0}$.Since $a, b, c$ are non-zero scalars,the vectors $\vec{u}, \vec{v}, \vec{w}$ are linearly dependent,which implies they are coplanar.For any three vectors $\vec{\alpha}, \vec{\beta}, \vec{\gamma}$,the cross products $\vec{\alpha} 	imes \vec{\beta}$,$\vec{\beta} 	imes \vec{\gamma}$,and $\vec{\gamma} 	imes \vec{\alpha}$ are coplanar if and only if $\vec{\alpha}, \vec{\beta}, \vec{\gamma}$ are coplanar.Therefore,the vectors $\vec{\alpha}, \vec{\beta}, \vec{\gamma}$ are coplanar.

If $a(\vec{\alpha} \times \vec{\beta}) + b(\vec{\beta} \times \vec{\gamma}) + c(\vec{\gamma} \times \vec{\alpha}) = \overrightarrow{0}$,where $a, b, c$ are non-zero scalars,then the vectors $\vec{\alpha}, \vec{\beta}, \vec{\gamma}$ are

Similar Questions

The scalar product of the vector $\hat{i}+\hat{j}+\hat{k}$ with a unit vector along the sum of vectors $2 \hat{i}+4 \hat{j}-5 \hat{k}$ and $\lambda \hat{i}+2 \hat{j}+3 \hat{k}$ is equal to $1$. Find the value of $\lambda$.

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\vec{0}$,then the value of $\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}$ is equal to

If $a \cdot i = a \cdot (i + j) = a \cdot (i + j + k)$, then $a = $

Let $\vec{a}=2 \hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=2 \hat{j}-3 \hat{k}$. If $\vec{b}=\vec{c}-\vec{d}$,$\vec{a}$ is parallel to $\vec{c}$,and $\vec{a}$ is perpendicular to $\vec{d}$,then $\vec{c}+\vec{d}=$

If the position vectors of the vertices of a triangle are $2\hat{i} - \hat{j} + \hat{k}$,$\hat{i} - 3\hat{j} - 5\hat{k}$,and $3\hat{i} - 4\hat{j} - 4\hat{k}$,then the triangle is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module