[3×2] Find if the scalar projection of on is units. The Cartesian equation of a line is: . Find the…

Find $\lambda$ if the scalar projection of $\vec{a} = \lambda\hat{\imath} + \hat{\jmath} + 4\hat{k}$ on $\vec{b} = 2\hat{\imath} + 6\hat{\jmath} + 3\hat{k}$ is $4$ units.

The Cartesian equation of a line is: $2x - 3 = 3y + 1 = 5 - 6z$. Find the vector equation of a line passing through $(7, -5, 0)$ and parallel to the given line.

Find the equation of the plane through the intersection of the planes $\vec{r} \cdot (\hat{\imath} + 3\hat{\jmath} - \hat{k}) = 9$ and $\vec{r} \cdot (2\hat{\imath} - \hat{\jmath} + \hat{k}) = 3$ and passing through the origin.