If (vec{a} times vec{b}) times vec{c} = vec{a | vedclass

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

Question

(C) Using the vector triple product formula,$(\vec{a} 	imes \vec{b}) 	imes \vec{c} = (\vec{a} \cdot \vec{c})\vec{b} - (\vec{b} \cdot \vec{c})\vec{a}

Vedclass · Accepted Answer

Parallel

Vedclass · Answer

(C) Using the vector triple product formula,$(\vec{a} 	imes \vec{b}) 	imes \vec{c} = (\vec{a} \cdot \vec{c})\vec{b} - (\vec{b} \cdot \vec{c})\vec{a}$.Also,$\vec{a} 	imes (\vec{b} 	imes \vec{c}) = (\vec{a} \cdot \vec{c})\vec{b} - (\vec{a} \cdot \vec{b})\vec{c}$.Given the equation $(\vec{a} 	imes \vec{b}) 	imes \vec{c} = \vec{a} 	imes (\vec{b} 	imes \vec{c})$,we equate the two expressions:$(\vec{a} \cdot \vec{c})\vec{b} - (\vec{b} \cdot \vec{c})\vec{a} = (\vec{a} \cdot \vec{c})\vec{b} - (\vec{a} \cdot \vec{b})\vec{c}$.Subtracting $(\vec{a} \cdot \vec{c})\vec{b}$ from both sides,we get:$-(\vec{b} \cdot \vec{c})\vec{a} = -(\vec{a} \cdot \vec{b})\vec{c}$.This implies $(\vec{b} \cdot \vec{c})\vec{a} = (\vec{a} \cdot \vec{b})\vec{c}$.Since $(\vec{b} \cdot \vec{c})$ and $(\vec{a} \cdot \vec{b})$ are scalars,this equation shows that $\vec{a}$ is a scalar multiple of $\vec{c}$.Therefore,$\vec{a}$ and $\vec{c}$ are parallel.

If $(\vec{a} \times \vec{b}) \times \vec{c} = \vec{a} \times (\vec{b} \times \vec{c})$,where $\vec{a}, \vec{b},$ and $\vec{c}$ are any three vectors such that $\vec{a} \cdot \vec{b} \neq 0$ and $\vec{b} \cdot \vec{c} \neq 0$,then $\vec{a}$ and $\vec{c}$ are:

Similar Questions

If $\bar{x} \cdot \bar{y} = 0$,then $\bar{x} \times (\bar{x} \times \bar{y}) = \dots$ where $|\bar{x}| = 1$.

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors such that no two of them are collinear and $(\vec{a} \times \vec{b}) \times \vec{c} = \frac{1}{3}|\vec{b}| |\vec{c}| \vec{a}$. If $\theta$ is the angle between vectors $\vec{b}$ and $\vec{c}$,then a value of $\sin \theta$ is:

If $a = i + j - k$,$b = i - j + k$,and $c = i - j - k$,then $a \times (b \times c) = \dots$

Let $\vec{a} = \hat{i} + \hat{j}$, $\vec{c} = \hat{i} - \hat{j}$ and a vector $\vec{b}$ be such that $\vec{a} \times \vec{b} = \vec{c}$ and $\vec{a} \cdot \vec{b} = 3$. Then $|\vec{b}| = $

$\overrightarrow{a} \times [\overrightarrow{a} \times (\overrightarrow{a} \times \overrightarrow{b})]$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module