Question

Which among the following given options is/are not flase?

• A. $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear.
• B. If t is a scalar, then $\overrightarrow{a}$ and $t\overrightarrow{a}$ are collinear
• C. $|-2\overrightarrow{a}|=-2|\overrightarrow{a}|$
• D. Magnitude of -3$\overrightarrow{a}$ is thrice that of $\overrightarrow{a}$. where $\overrightarrow{a}$ is a vector.

Answer 1

Answer: (B), (D)

The correct options are
B If t is a scalar, then $\overrightarrow{a}$ and $t\overrightarrow{a}$ are collinear
D Magnitude of -3$\overrightarrow{a}$ is thrice that of $\overrightarrow{a}$. where $\overrightarrow{a}$ is a vector.

Option A is not correct because $\overrightarrow{a}$ and $\overrightarrow{b}$ can be such that $|\overrightarrow{a}\times \overrightarrow{b}|$ $\ne$0

OPtion B

$|\overrightarrow{a}\times \overrightarrow{ta}|$

t$|\overrightarrow{a}\times \overrightarrow{a}|$

0 because $|\overrightarrow{a}\times \overrightarrow{a}|$ =0

option C

also false Let $\overrightarrow{a}=\hat{i}$

$-2\overrightarrow{a}=-2\hat{i}$
$\left|\overrightarrow{-2a}\right|=\sqrt{(-2{)}^2}=2$

but $-2\left|\overrightarrow{a}\right|=-2\times \sqrt{1^2}=-2$

SO $\left|\overrightarrow{-2a}\right|$ $\ne$ $-2\left|\overrightarrow{a}\right|$

Option D is correct

$|-3\overrightarrow{a}|=\sqrt{(-3{)}^2}=3$

3$\left|\overrightarrow{a}\right|=3\sqrt{(1{)}^2}=3$