Ncert Solutions for Class 12
Three Dimensional Geometry
Three Dimensional Geometry
1. Find the angle between the lines whose direction ratios are a,b,c and b–c, c–a, a–b.
2. Find the equation of a line parallel to x-axis and passing through the origin.
3. If the lines (frac{x-1}{-3}=frac{y-2}{2k}=frac{z-3}{2}) and (frac{x-1}{3k}=frac{y-1}{1}=frac{z-6}{-5}) are perpendicular, find the value of k.
4. Find the shortest distance between lines
(vec{r}=6hat{i}+2hat{j}+2hat{k}+lambdaleft(hat{i}-2hat{j}+2hat{k}right)) and (vec{r}=-4hat{i}-hat{k}+muleft(3hat{i}-2hat{j}-2hat{k}right)).
5. Find the vector equation of the line passing through the point (1,2,–4) and perpendicular to the two lines:
(frac{x-8}{3}=frac{y+19}{-16}=frac{z-10}{7}) and (frac{x-15}{3}=frac{y-29}{8}=frac{z-5}{-5}).