Mathematics Lab Activity-13 Class XII
Mathematics Laboratory Activities 12 on Three Dimensional Geometry for class XI Non-Medical students with complete observation tables strictly according to the CBSE syllabus.
Chapter - 11
three dimensional geometry
Activity - 13
Objective
To measure the shortest
distance between two skew lines and verify it analytically.
Material Required
A piece of plywood of size
30cm x 20 cm, a squared paper, three wooden blocks of size 2cm x 2cm x 2cm each
and one wooden block of size 2 cm x 2 cm x 4cm, wires of different lengths, set
squares, adhesive, pen/pencils, etc.
Procedure
1. Paste a squared paper on a piece of
plywood.
2. On a squared paper, draw two lines OA and
OB to represent x- axis, and y-axis, respectively.
3. Name the three blocks of size 2cm x 2cm x 2cm as I, II and III, name the
other wooden block of size 2 cm x 2 cm x 4cm as IV.
4. Place blocks I, II, III such that their
base centres are at the points (2, 2), (1, 6) and (7, 6), respectively, and block
IV with its base centre at (6, 2).
5. Place a wire joining the points P and Q,
the centres of the bases of the blocks I and III and another wire joining the
centres R and S of the tops of blocks II and IV as shown in figure 13.1. These
two wires represent two skew lines as these are connected in different planes.
6. Take a wire and join it perpendicularly
with the skew lines and measure the actual distance.
7. A set square is placed in such a way that
its one perpendicular side is along the wire PQ.
8. Move the set-square along PQ till its
other perpendicular side touches the other wire.
9. Measure the distance between the two
lines in this position using set-square. This is the shortest distance between
two skew lines.
10. Analytically, find the equation of line joining
P(2, 2, 0) and Q(7, 6, 0) and other line joining R(1, 6, 2) and S(6, 2, 4) and find
S.D. using the formula
.\left(\overrightarrow{b_{1}}\times\overrightarrow{b_{2}}\right)}{\left|\overrightarrow{b_{1}}\times\overrightarrow{b_{2}}\right|}\right|)
. The distance obtained in two cases will be the same.
Observations
1.
Coordinates
of point P are (2, 2, 0)
2.
Coordinates
of point Q are (7, 6, 0)
3.
Coordinates
of point R are (1, 6, 2)
4.
Coordinates
of point S are (6,
2, 4)
5.
Equation
of the line PQ is = 
6.
Equation
of the line RS is = 
7.
Shortest
distance between PQ and RS analytically = 3.0476 cm
Shortest distance by actual measurement = 3 cm
Result
Here we conclude that the
shortest distance between two lines calculated analytically and by actual
measurement is approximately same.
Applications
This activity can be used
to explain the concept of skew lines and of shortest distance between two lines
in the space.
VIVA – VOICE
Q1. What are skew lines ?
Ans. Skew lines are those lines which are neither intersecting nor parallel.
Q2. What is shortest distance between teo lines ?
Ans. It is that distance which is shortest to all the distances between two points lying on both lines.
Q3. What is the shortest distance between two intersecting lines ?
Ans. Zero.
Q4. Is shortest distance between two lines perpendicular to both the lines ?
Ans. Yes
Q5. Write down example of two skew lines ?
Ans. A pair of lines through opposite edges of a regular tetrahedron.
Q6. Write down shortest distance between two parallel lines 
and 
. Ans.
Q7. Write down formula for shortest distance between lines 
and 
. Ans.
.(\vec{b_{1}}\times\vec{b_{2}})|}{|\vec{b_{1}}\times\vec{b_{2}}|})
THANKS FOR YOUR VISIT
PLEASE COMMENT BELOW
Comments
Post a Comment