$$ \text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|= $$

The angle between the vectors $$\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ and $$\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$$ is

If the vectors $$\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\mathbf{c}=m \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ are coplanar, then the value of $$m$$ is

$$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}$$ and $$\mathbf{c}=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$, then unit vector parallel to $$\mathbf{a}+\mathbf{b}-\mathbf{c}$$ but in opposite direction is