Two vectors $${\overrightarrow P }$$ and $${\overrightarrow Q }$$ have equal magnitudes. If the magnitude of $${\overrightarrow P + \overrightarrow Q }$$ is n times the magnitude of $${\overrightarrow P - \overrightarrow Q }$$, then angle between $${\overrightarrow P }$$ and $${\overrightarrow Q }$$ is :

If $$\overrightarrow A $$ and $$\overrightarrow B $$ are two vectors satisfying the relation $$\overrightarrow A $$ . $$\overrightarrow B $$ = $$\left| {\overrightarrow A \times \overrightarrow B } \right|$$. Then the value of $$\left| {\overrightarrow A - \overrightarrow B } \right|$$ will be :

In an octagon ABCDEFGH of equal side, what is the sum of

$$\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} + \overrightarrow {AG} + \overrightarrow {AH} $$,

if, $$\overrightarrow {AO} = 2\widehat i + 3\widehat j - 4\widehat k$$

Let $$\left| {\mathop {{A_1}}\limits^ \to } \right| = 3$$, $$\left| {\mathop {{A_2}}\limits^ \to } \right| = 5$$ and $$\left| {\mathop {{A_1}}\limits^ \to + \mathop {{A_2}}\limits^ \to } \right| = 5$$. The value of $$\left( {2\mathop {{A_1}}\limits^ \to + 3\mathop {{A_2}}\limits^ \to } \right)\left( {3\mathop {{A_1}}\limits^ \to - \mathop {2{A_2}}\limits^ \to } \right)$$ is :-