If vectors $$\bar{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$$ and $$\bar{c}=3 \hat{i}+\hat{j}+2 \hat{k}$$ are such that, $$\bar{a}+\lambda \bar{b}$$ is perpendicular to $$\bar{c}$$, then $$\lambda=$$

If $$\bar{a}=3 \hat{i}-5 \hat{j}, \bar{b}=6 \hat{i}+3 \hat{j}$$ are two vectors and $$\bar{c}$$ is a vector such that $$\bar{c}=\bar{a} \times \bar{b}$$, then $$a: b$$ : is

If $$|\bar{a}|=3,|\bar{b}|=4,|\bar{a}-\bar{b}|=5$$, then $$|\bar{a}+\bar{b}|=$$

$$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are vectors such that $$|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=4,|\overline{\mathrm{c}}|=3$$ and each is perpendicular to the sum of the other two, then $$|\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}|^2=$$