 Hello friends, myself Professor S.P. Mankani, Assistant Professor, Department of Mechanical Engineering, Walsh and Institute of Technology, Solaapur. Today we are going to study the projection of lines. At the end of this lecture, students will be able to draw front view, top view of a line without apparent or at two angles. The top view of a 75 millimeter long line, AB measures 65 millimeter. And its front view measures 50 millimeter. Its one end A is in the HP and 12 millimeter in front of VP. Draw the projection of line AB and determine its inclination with HP and VP. So here also, he has not given any angles directly only as given as a dimensions of the lines. The important thing here you have to understand as there will not be any angles is given in this problem is concerned. So now the actual solution for this particular problem. So the given condition is the top view of a line is 75 millimeter long, the top view of a 75 millimeter long line. So this is the true length is 75 millimeter. Major 65 millimeter means that length of the top view has given as a 65 millimeter. So that is top view length is 65 millimeter. While its front view measures 50 millimeter, front view has given as a 50 millimeter. And A is in the HP, you are expected to write the first as a given condition. Then you start the solution of this particular problem is concerned. So here to draw front view and top view of the line AB and find the angle theta and phi. Theta is the angle made by the line with the HP and phi is the angle made by the line with the VP. So now first you draw the XY line. So then we have to locate the points. You take it anywhere on this XY line as a point A point. So as is given in the problem as point A is in the HP, I have taken this is the point is on the XY line above the XY line. Means it is touching from the above the XY line. It is coming here. So you are located at the point A point. This we are going to be writing it as a A dash with the reason that this is the front view location. It is a front view location. So now we have to take it as the dimension is given in the problem as and total millimeter in front of VP got to measure from the XY line below the XY line. All the measurement to the VP has to be measured from the XY line below the XY line. This is the total millimeter position you have taken it. So this point is at a distance of 12 millimeter in front of the VP. So now you have to give the naming as A point. Here it is A dash as a front view and A as a top view. So this is 12 millimeter distance. So now we have to move for the further step. So now here the important thing is draw a line AB1 parallel to the XY line and the length as 65 millimeter parallel to the XY line below the XY line from this particular point A. Which is a length of 65 millimeter because when top view is parallel to the XY line, front view is given as a true length. When this is suppose you are taking this as a line any line which is parallel to the XY line at the same time in the front you are going to be getting it as a true length of that particular line. So now you have to draw this line as a length of 65 millimeter. So from this particular point you have to take 65 millimeter. Locate this point as P1 point. This is a length of 65 millimeter. So now if you project this line in the upward direction and then from this particular point if you take it you will get this as a true length which is already given in the problem as 75 millimeter. This point helps us to locate the point B1 dash. B1 dash that is in the front view to locate the point in the front view. We are expected to project this line in the upward direction. Then keep the compass at this particular point take 75 millimeter as a length then you cut it this line. So while you cut it this line this is a position of a B1 dash. This is a position of a B1 dash. That is nothing but the length of the line 75 millimeter making a certain degrees of angle with the horizontal plane because above the XY line if it makes the angle it is we are going to be calling it as a angle made by the line with the HP. So join this point and give the notation as B1 dash and this length is 75 millimeter. So now he is expected in the problem as determine its inclination with HP and VP. So this angle is nothing but the angle made by the line with the horizontal reference plane. This angle is angle made by the line with the horizontal reference plane. So this is what we are going to be representing here as a theta angle. This is expected in the problem. So now you got this as angle as theta which is around 31 degree plus or minus 1 degree is considerable as a error. But preferably as much as possible you are going to be getting as a accurate angles only. Here it is a theta as 31 degree. One condition you have got it. So it will go for another condition in the top you side. So now this is the point as just you draw the locus of the B point. It is a locus of B point. This line is parallel with the XY line. We are going to be calling this as a locus means this is a position of B at this particular distance from the XY line. So after drawing this locus line we are expected to get the front view line. So in the problem as the top view length is 65 millimeter while its front view length is 50 millimeter. We are written as a front view length as 50 millimeter. Keep the compass here. Take it 50 millimeter length and draw the line. So you are going to cut it this one line the locus of this line and you are going to get this point as a B dash point. A dash B dash is giving as a front view length. A dash B dash is giving as a front view length of the line. From here A dash B dash as a front view length of the line is concerned. So join this line. Join this line. You are going to get it this as a A dash B dash as the front view length line which is given as 50 millimeter length. By measuring 50 millimeter cut this one the locus line and you will get it this as a point. Now this is A dash B dash line. So now you have to project this line in the downward direction so that on this particular projector you are expected to get the position of a top view point for B. If you are going to draw this projector in the downward direction the position of the B point you are going to get it in the top view condition. The length of the top view is given as 65 millimeter. The length of the top view is given as a 65 millimeter in the problem. So meanwhile you are going to bring this projector here it is the projector the position is there. Keep the compass here you take it this length and draw the arc and this position and this position is also going to cut it. So now this is 65 millimeter you just draw this one line and you take it 65 millimeter and you cut it. Now you are going to get it as this line as a position of B point AB is the top view length line AB is the length of the top view we are going to be writing it as a top view length of the line. So now let me know how you can get it without using this projector can you understand this one. Now without drawing this arc how can you get the position of this particular point is considered already given a clue in the explanation it is expected as how to get this point without a drawing this arc how you are going to get it this position means draw the projector line from here in the downward direction you will get it this as a projector line take it 65 millimeter then you cut it you will get it the same position of the point is considered you are going to get it as a same position the point as a AB as a length of the this line in the top view it looks as a 65 millimeter actually line length is 75 millimeter still you are not located that particular line in the top view. So now you have to draw this as a locus at this particular point as a B point draw the locus this is the locus of B point. So now take it 75 millimeter as a length keep the compass here cut it this locus line so that you are going to be getting this as AB1 this is the position of the actual length of the line you are going to be calling this as a this is the length true length of the line this is the true length of the line and this is the true inclination this is the true inclination they are expected in the problem this theta you have calculated now you have to measure this angle as a phi angle so this angle as phi angle. So measure this angle and you write it separately the expected answer you have to write it separately by highlighting those particular information is concerned. So measure this angle this angle is approximately getting it as a 49 degree this angle you are going to getting as a 49 degree write it separately as a 49 degree as a angle. So now here you have completed the problem just you have a recheck over the complete problem the given conditions are 75 millimeter length you have taken 75 millimeter as a true length 65 millimeter as a top U length 65 millimeter you have taken as a top U length and 50 millimeter as a front U length 50 millimeter you have taken as a front U length means you are full feed all the given dimensions you have taken as a correctly then the expected answer as 31 degree as a theta which is the angle made by the line with the HP as 31 degree and similarly angle made by the line with the VP as 49 degree means you have written both the answers and you have considered all the information given in the problem. One more condition you have forgotten as 12 millimeter length is given and you take it that 12 millimeter is in front of the VP. So that this concludes the problem only with the information as maintain this line as a dark line, this line as a dark line top you length and the front you length you have to draw as a dark line and this line as a medium thickness line and even x y line as a medium thickness line all the rest of the informations are construction lines that has to be drawn as a thin lines only. Thank you.