If $\mathbf{a}+\mathbf{b}+\mathbf{c}=0,|\mathbf{a}|=3,|\mathbf{b}|=5,|\mathbf{c}|=7$, then the angle between $\mathbf{a}$ and $\mathbf{b}$ is

If $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}},-12 \hat{\mathbf{i}}-\hat{\mathbf{j}}-3 \hat{\mathbf{k}},-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\lambda \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are the position vectors of four coplanar points, then $\lambda=$

Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ be two vectors. If the orthogonal projection vector of $\mathbf{a}$ on $\mathbf{b}$ is $\mathbf{x}$ and orthogonal projection vector of $\mathbf{b}$ on $\mathbf{a}$ is $\mathbf{y}$, then $|\mathbf{x}-\mathbf{y}|=$

II. If the points with position vectors $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{k}}$, $\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}$ are coplanar, then the magnitude of the vector $6 \lambda \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$ is