# Lecture - 12 Chapter 11 Three Dimensional Geometry

“Whenever you find yourself on the side of the majority, it is time to pause and reflect.” –Mark Twain

**9.** Find the angle between the line \(\frac{x+1}{2}=\frac{y}{3}=\frac{z-3}{6}\) and the plane 10x+2y-11z=3

**10.** Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane \(\vec{r}.(\hat{i}+2\hat{j}-5\hat{k})+9=0\).

**15.** If O be the origin and the coordinates of P be (1, 2, −3), then find the equation of the plane passing through P and perpendicular to OP.

**16.** Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes \(\vec{r}.(\hat{i}-\hat{j}+2\hat{k})=5\) and \(\vec{r}.(3\hat{i}+\hat{j}+\hat{k})=6\) .

**19.** If a line makes angles \(\alpha,\beta,\gamma\) with the positive direction of the coordinate axes; then find the value of \({sin}^2{\alpha}+{sin}^2{\beta}+{sin}^2{\gamma}\).