Short Quiz

Assertion \((A)\) : The vectors \(\overrightarrow{\mathrm{a}}\) and \((-2 \overrightarrow{\mathrm{a}})\), where \(\overrightarrow{\mathrm{a}} \neq \overrightarrow{0}\) are collinear vectors.
\(\operatorname{Reason}(R): \quad \overrightarrow{\mathrm{a}} \cdot(-2 \overrightarrow{\mathrm{a}})=0\).

If \(|\overrightarrow{\mathrm{a}}|=2\) and \(-3 \leq \mathrm{k} \leq 2\), then \(|\mathrm{k} \overrightarrow{\mathrm{a}}| \in\) :

For any two vectors \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\), which of the following statements is always true?

For two vectors \(\vec{a}\) and \(\vec{b}\)
Assertion (A) : \(|\vec{a} \times \vec{b}|^2+(\vec{a} \cdot \vec{b})^2=|\vec{a}|^2|\vec{b}|^2\)
Reason (R): : \(|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}) \tan \theta,\left(\theta \neq \frac{\pi}{2}\right)\)