If the vectors $$2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\lambda \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ are coplanar, then the value of $$\lambda$$ is

If $$|\mathbf{a}|=16,|\mathbf{b}|=4$$, then $$\sqrt{|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2}=$$

If the angle between $$\mathbf{a}$$ & $$\mathbf{b}$$ is $$\frac{2 \pi}{3}$$ and the projection of $$\mathbf{a}$$ in the direction of $$\mathbf{b}$$ is $$-$$2 , the $$|\mathbf{a}|=$$

A unit vector perpendicular to the plane containing the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$ is