# 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 $${sin}^2{\alpha}+{sin}^2{\beta}+{sin}^2{\gamma}$$.