If two vectors $$\overrightarrow P = \widehat i + 2m\widehat j + m\widehat k$$ and $$\overrightarrow Q = 4\widehat i - 2\widehat j + m\widehat k$$ are perpendicular to each other. Then, the value of m will be :

Two vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ have equal magnitudes. If magnitude of $$\overrightarrow A $$ + $$\overrightarrow B $$ is equal to two times the magnitude of $$\overrightarrow A $$ $$-$$ $$\overrightarrow B $$, then the angle between $$\overrightarrow A $$ and $$\overrightarrow B $$ will be :

$$\overrightarrow A $$ is a vector quantity such that $$|\overrightarrow A |$$ = non-zero constant. Which of the following expression is true for $$\overrightarrow A $$ ?

Which of the following relations is true for two unit vector $$\widehat A$$ and $$\widehat B$$ making an angle $$\theta$$ to each other?