Consider overrightarrow{r}, overrightarrow{a} | vedclass

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

Question

(D) Given that $\overrightarrow{r} \cdot \overrightarrow{a} = 0$,this implies that $\overrightarrow{r}$ is perpendicular to $\overrightarrow{a}$.From

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(D) Given that $\overrightarrow{r} \cdot \overrightarrow{a} = 0$,this implies that $\overrightarrow{r}$ is perpendicular to $\overrightarrow{a}$.From $|\overrightarrow{r} 	imes \overrightarrow{b}| = |\overrightarrow{r}| |\overrightarrow{b}|$,we know that $\sin 	heta = 1$,where $	heta$ is the angle between $\overrightarrow{r}$ and $\overrightarrow{b}$. Thus,$\overrightarrow{r}$ is perpendicular to $\overrightarrow{b}$.Similarly,from $|\overrightarrow{r} 	imes \overrightarrow{c}| = |\overrightarrow{r}| |\overrightarrow{c}|$,we conclude that $\overrightarrow{r}$ is perpendicular to $\overrightarrow{c}$.Since $\overrightarrow{r}$ is a non-zero vector perpendicular to $\overrightarrow{a}, \overrightarrow{b},$ and $\overrightarrow{c}$,these three vectors must lie in a plane perpendicular to $\overrightarrow{r}$.Therefore,$\overrightarrow{a}, \overrightarrow{b},$ and $\overrightarrow{c}$ are coplanar.For any three coplanar vectors,their scalar triple product is zero.Thus,$[\overrightarrow{a} \overrightarrow{b} \overrightarrow{c}] = 0$.

Similar Questions

If three conterminous edges of a parallelepiped are represented by $\vec{a} - \vec{b}$,$\vec{b} - \vec{c}$,and $\vec{c} - \vec{a}$,then its volume is

If $a, b$ and $c$ are three non-coplanar vectors,then $(a + b + c) \cdot [(a + b) \times (a + c)]$ is equal to

The volume of the parallelepiped whose edges are represented by $-12i + \alpha k$,$3j - k$,and $2i + j - 15k$ is $546$. Then $\alpha = $

If $[\bar{a} \times \bar{b} \quad \bar{b} \times \bar{c} \quad \bar{c} \times \bar{a}] = \lambda [\bar{a} \quad \bar{b} \quad \bar{c}]^2$,then $\lambda$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module