[3×2] Find the area of the parallelogram whose adjacent sides are given by the vectors and . Find…

Find the area of the parallelogram whose adjacent sides are given by the vectors $\vec{a} = 3\hat{\imath} + \hat{\jmath} + 4\hat{k}$ and $\vec{b} = \hat{\imath} - \hat{\jmath} + \hat{k}$.

Find the angle between the line $\frac{x+1}{2} = \frac{y}{3} = \frac{z-3}{6}$ and the plane $2x + 3y - 5z = 4$.

Find the Cartesian equation of the line passing through the points $(-1, 0, 2)$ and $(3, 4, 6)$.