3 3-D Geometry - Skew lines & Shortest Distance.pptx

Maths vector ppt

1. Mathematics –Class XII Unit IV-Vector & 3D Chapter 11 -Three Dimensional Geometry Sub topic-Skew lines &Shortest distance

2. LINES Skew lines and its Definition. Shortest distance and its Definition. Shortest distance between two skew lines . Assignment Outline:

3. SKEW LINES B A

4. SKEW LINES and THE SHORTEST DISTANCE Two lines neither intersecting nor parallel are called ” Skew Lines”. . CONTINUE

5. The shortest distance between two skew lines is perpendicular length between them.

6. Let and be the equations of two given lines .

7. Let ‘d’ be the shortest distance between the given two skew lines, then.

8. CONTINUED ( a 2 – a 1 ) . b 1 x b 2 d = ----------------------- | b 1 x b 2 | which the shortest distance between the given two skew lines. BACK

9. HERE LINE 1 AND LINE 2 ARE SKEW LINES AND ARE LYING IN DIFFERENT PLANES

10. Q1 .. Find the shortest distance between the two lines whose vector equations are = ( i+2j +3k ) + λ ( i -3j +2k ) and = (4i +5j+ 6k ) -µ (2i +3j +k) Q2 . Find the shortest distance between the two lines whose vector equations are = i (1+2λ) +j(1-λ )+λ k = i (2+3 µ)+j(1-5 µ)+(-1+2 µ)k ASSIGNMENT

11. Q3.Two bikers are running at the speed more than allowed on the road along the lines, = -5i -3j +6 k + t(i + 4 j --9k) and = 2i - j + k + µ(2i + j + 2k). Using shortest-distance formula check whether they meet to an accident or not ?