1. Tardigrade
  2. Question
  3. Mathematics
  4. Statement 1: The vectors veca, vecb and vecc lie in the same plane if and only if veca. ( vecb× vecc) = 0 Statement 2: The vectors vecu and vecv are perpendicular if and only if vecu . vecv = 0 where vecu × vecv is a vector perpendicular to the plane of vecu and vecv

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Statement 1 : The vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$ lie in the same plane if and only if $\vec{a}. \left(\vec{b}\times\vec{c}\right) = 0$
Statement 2 : The vectors $\vec{u}$ and $\vec{v}$ are perpendicular if and only if $\vec{u} .$$\vec{v}$ = 0 where $\vec{u} \times$$\vec{v}$ is a vector perpendicular to the plane of $\vec{u}$ and $\vec{v}$

AIEEEAIEEE 2012Vector Algebra

Solution:

Statement - 1
The vectors $\vec{a}, \vec{b}$ and $\vec{c}$ lie in the same plane.
$\Rightarrow \vec{a}, \vec{b}$ and $\vec{c}$ are coplanar.
We know, the necessary and sufficient conditions for three vectors to be coplanar is that $\left[\vec{a} \vec{b} \vec{c}\right] = 0$
$i. e. \vec{a}\cdot \left(\vec{b} \times \vec{c}\right) = 0$
Hence, statement-1 is true.