1. Engineering Graphics 2018-19-I
Lecture 18
TA101A
Engineering Graphics I By
Dr. Mukesh Sharma
Professor
DEPARTMENT OF CIVIL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY KANPUR
KANPUR , INDIA

2. aH bH 1H 2H 3H 4H H F aF bF 1F 2F 3F 4F XH YH YF XF
A Line in a plane – if a line is in the plane, all points of intersection should stay aligned in all views

3. Construct a line parallel to a planebH 1H dH cH aH 2H H F aF dF 2F cF bF 1F
Line 1-2 in top view and Point 1F is given
See we forced the line 1-2 to be parallel to line b-d in front view
As a result, line 1-2 is parallel to the given plane (abc)

4. A line perpendicular to a plane
Very useful in finding shortest distance from a point to a plane pH 1H 2H 3H 4H H F oH oF pF TL EV
4F3F
1F2F
900
A line is perpendicular to plane when the line is in true length at a 900
angle to an edge view of the plane. Line OP is perpendicular to plane
How to draw a perpendicular from a point with this concept?

5. Draw a perpendicular to a plane from point – Recall edge view of plane and perpendicular at 900 needed
PARALLEL OH 2H
TL(?. Yes)
Should be in TL OA 3H
3A2A pH 1H PA
900 H A d 4H EV H
4A1A F d 2F 3F pF
Get the edge of plane
See if any line in TL on the plane
See through the line and project all points
Line 2-3 in top view in TL in
In aux view take distance from Front and locate points
Draw a perpendicular from OA on EV ~ OA PA (in TL?)
Project PA to Top view (see the arrows)
Project PH to Front view see PF 1F 4F OF

6. Visibility of perpendicular OPOH
In horizontal and front views
Part of the OP can be behind the plane thus become dash
Methodology: For Horz. View bring the point on OP drop it down to Front view
And see which line you encounter first
Line appearing first is above. The line appearing second is behind
and thus should be dash A 2H TL 3H pH 1H 4H C B H F 2F 3F pF 1F 4F OF

7. Angle Between line and plane5H 4C 2H TL
True
Angle TL EV 3H 3C IC 2C
Sight
┴ to
Line 4-5 IH 4H H 4F F 3F 3A C 5C 2F B H 3B A 2A 4A 5A 5B 2B IF 5F EV 4B A B TS IA IB
Angle Between line and plane

8. Recap of Concept – Did you get this?IB 2B 3B 4B rB sB B A
IA2A
4A3A rA sA TL EV 5B 6B 7B 8B tB uB B A
5A6A
8A7A tA uA EV
NOT TL
True
Angle
NOT
True Angle A
Recap of Concept – Did you get this?

9. Objective find angle between two planes6H 4H 2H
Line 1-2 is common to both the Planes. TL 3H 5H 1H H F
1F2F EV EV
5F6F
True Angle
3F4F
Concept – if we can project the planes in their EVs
The angle between the EVs will be the true angle between the planes

10. Angle between Two Planes
Get edge views of the planes
Do you see common line to be in TL
It is ab – see through it (e.g. hinge line
Be perpendicular to TL)
From EVs find true angle between planes dH aH bH cH H F cF dF aF F I TL cI dI bF
True
angle EV EV
aI,bI

11. Angle between planes – General CasedI dI D2 DH H AH 1
True
angle cH 1 2 EV DI
A2B2 BH EV C2 AI TL H BI F DF d d CI BF AF CF
Angle between planes – General Case

12. Concept: Shortest Distance from a point to a line
900 OH
900 H PH oH A 3H
Parallel TL OA
Parallel PH IH TL 4H TL H H
4APA3A F F PF
IFPF2F 3F 4F A B TL OF OF
Concept: Shortest Distance from a point to a line

13. Finding shortest Distance from a point to a lineOH bH H pH I
b2p2a2 bI aH TL pI 1 2 oI TL
900 aI
Parallel oI H F aF pF bF oF
Concept: Get the line in TL and keep projecting the point and then draw
Perpendicular from the point on the obtained TL.
Next step is to get the TL in point view and you will see the shortest distance (point to line)
Project the perpendicular in Front and Top view

14. + Concept – Shortest Distance between two lines
What is the condition that should be met? 2H 3H OH PH TL 4H IH
Parallel H F + 4F OF
IF2F
900 TL PF 3F

15. Shortest Distance between two lines – most general casebH H oH I dH 1 2 aH d2
b2o2a2 cH pH dI bI TL TL oI
900 p2 aI
Parallel pI c2 H F aF cI oF dF pF cF bF
Shortest Distance between two lines – most general case

16. Intersection of a line and plane – EV methodTL 2A 5H 1A 1H H 5A F 1F 2F
2’F 4F 5F 3F
Intersection of a line and plane – EV method

17. Intersection of Line and Plane: Cutting Plane methodXH 2H YH 1H 5H H F 1F C YF 4F 2F 5F XF B 3F