Statement 1 : The vectors a , b and c lie in the same plane if an… - Vidyadip

MCQ

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 $\vec v$

A
Statement $1$ is false, Statement $2$ is true.
B
Statement $1$ is true, Statement $2$ is true,Statement $2$ is correct explanation for Statement $1$ .
✓
Statement $1$ is true, Statement $2$ is false.
D
Statement $1$ is true, Statement $2$ is true, ,Statement $2$ is not a correct explanation for Statement $2$

✓

Answer

Correct option: C.

Statement $1$ is true, Statement $2$ is false.

c
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 $[\vec{a} \vec{b} \vec{c}]=0$

i.e. $\vec{a} \cdot(\vec{b} \times \vec{c})=0$

Hence, statement- $l$ is true.

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