3D GEOMETRY: CLASS 12TH:DIRECTION RATIOS AND DIRECTION COSINES

3D GEOMETRY:
Q1. Define Direction Ratios and direction cosines                      (2)
Q2. Find the Direction Ratios and direction cosines of line passing through the points A(-4,2,3)and B(1,3,-2)                                        (2)
Q3. Show that the points A(-7,4,-2), B(-2,1,0), C(3,-2,2) are collinear.  (2)

Q4. If a line makes angles 90⁰, 135⁰ and 45⁰ with X,Y and Z axis respectively.
      find its direction cosines        (2)       
Q5. If the line makes angles α,β,γ with coordinate axes Prove that

 i)Sin²α+sin²β+sin²γ=2
 ii)Cos2α+cos2β+cos2γ = -1                  (4)

Q6. If l,m,n are directions cosines of a line then l²+m²+n² = 1                          (3)

Q7. Find the direction cosines of the line which is perpendicular to the lines with direction rarios-1,2,2 and 0,2,1.                           (3)

Q8. Show that the angle between any two diagonals of a cube is cos^-1(1/3).                                                (2)