If the vectors $$\vec{a}=2 \hat{i}+p \hat{j}+4 \hat{k}$$ and $$\vec{b}=6 \hat{i}-9 \hat{j}+q \hat{k}$$ are collinear, then $$p$$ and $$q$$ are

If $$|\vec{a}|=4,|\vec{b}|=5$$, then the values of $$k$$ for which $$\vec{a}+k \vec{b}$$ is perpendicular to $$\vec{a}-k \vec{b}$$ are

The vectors $$\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}$$ and $$\overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$$ are the sides of a triangle $$\mathrm{ABC}$$. The length of the median through $$\mathrm{A}$$ is

If $$\bar{a}=2 \hat{i}+3 \hat{j}-\hat{k}, \bar{b}=-\hat{i}+2 \hat{j}-4 \hat{k}$$ and $$\bar{c}=\hat{i}+\hat{j}-2 \hat{k}$$, then $$(\bar{a} \times \bar{b}) \cdot(\bar{a} \times \bar{c})=$$