The angle between the lines $$\frac{x-1}{4}=\frac{y-3}{1}=\frac{z}{8}$$ and $$\frac{x-2}{2}=\frac{y+1}{2}=\frac{z-4}{1}$$ is

If the line $$r=(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})+\lambda(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}})$$ is parallel to the plane $$r \cdot(3 \hat{i}-2 \hat{\mathbf{j}}+m \hat{\mathbf{k}})=10$$, then the value of $$m$$ is

The points $$A(-a,-b), B(0,0), C(a, b)$$ and $$D\left(a^2, a b\right)$$ are

The cosine of the angle included between the lines $$\mathbf{r}=(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}})+\lambda(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$$ and $$\mathbf{r}=(\hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}})+\mu(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-6 \hat{\mathbf{k}})$$ where $$\lambda, \mu \in R$$ is.