 Hello friends, I am Professor S. P. Mankani, Assistant Professor, Department of Mechanical Engineering, Walsh and Institute of Technology, Solapur. So today we are going to study the numericals on projection of lines. So at the end of this lecture, students will be able to draw front view, top view of the given line and also show the corresponding apparent angles. Another question, top view of a 75 millimeter long line CD measures 50 millimeter and C is in HP and 50 millimeter in front of VP and D is 15 millimeter in front of VP and it is above HP. Draw projection of line CD and find angles with HP and VP. So in the given problem, top view of a line 75 millimeter means this is the true length of the given line of a line naming is given as CD and it measures 50 millimeter. The meaning of this one is the actual length is 75 millimeter, it measures, it looks as a 50 millimeter and C is in HP and 50 millimeter in front of VP and C is in HP means we have to consider the C point on the XY line reference line and 50 millimeter in front of VP means 50 millimeter, we have to measure it from the XY line as a distance and D is 15 millimeter in front of the VP and it is above HP, we have to take it this D point so as far as 15 millimeter in front of the VP and above the HP. So now we have to proceed for the actual drawing. So here we have to draw XY line first. So after drawing XY line, we are going to be measuring as a top view of a line 75 millimeter long CD measures 50 millimeter and C is in HP and this is important as 50 millimeter in front of the VP, you are taken as a 50 millimeter from XY line below the XY line with the reason that any distance is from the VP or to measure it from the XY line below the XY line as any distance from the HP, we are going to be measuring it from the XY line above the XY line. Now it is given as a 50 millimeter in front of the VP, the point C is given as 50 millimeter in front of the VP or to measure this as a 50 millimeter below this XY line and make it here as a one locus line. So then we are going to be taken this as a just reference line. In the problem it is given as end C is in the HP, we have to take it that end C on the XY line because any distance from the horizontal plane we are going to be measuring it from the XY line means now the given problem is given as a the distance from the horizontal reference plane is 0 as if it is available on the XY line, you have taken this as a C dash all the front view information you are going to be writing notations with the dash mark and all the top view are going to be notating given the notation as without dash mark. So here we are going to be taken this point as 15 millimeter in front of the VP so this distance is given as point D is 15 millimeter in front of the VP, you are taken this as a 15 millimeter then draw the locus line here. Just now we are representing this one as 50 millimeter distance and 15 millimeter distance and we are located here as a point C dash it is just a the given conditions. So now we have to proceed with the these given conditions. So here in this problem he has not given any angle the important thing is in this problem he has not given any angle only as given as a dimensions of lengths of the line top view as well as in the true length. So now based on this one we are going to be locating this point as a C point. So after locating this C point you can take it anywhere on this line but you are already located this point as a C dash here that is the reason projection of this one wherever it will cut there only are expected to take this C point. After locating C point and the given length of the line is 75 millimeter so based on that one take the distance from the compass keep the compass at C point and you cut it the locus of this D line. So wherever it will cut that point you have to locate it as D1 point because we are writing this as a without any dash mark it is a D1 point. So D1 point we are going to get it D1 point we are keeping this as a compass at C and taking 75 millimeter length and we are going to cut it this line. So this is a locus of D point which is at 15 millimeter from the vertical plane. So this one line are located as a 75 millimeter length and now this angle this is expected in the problem we will see it this one later on. So now we have to go for based on this one as a C point you have got it and this point you have got it now. So now one more information is given as top view of a line 75 millimeter long line C D measures 50 millimeter means this is apparent length he has given it. So this one by keeping compass here at a point C so we have to cut it this locus line anywhere on this line as per the given distance 50 millimeter you have to measure it from the compass keep the compass at C point and then you have to cut it this line here. So this is a D point. So C D length is 50 millimeter C D length is 50 millimeter he has given in the problem C D length is 50 millimeter you have to cut it this line and this you are going to be locating it as a top view length T V L you have to represent this one top view length and this is a true length. You have got a top view length and true length in the case of top view. So now we have to proceed this one. So as far as the front view is concerned anywhere on this particular projector the D point has to come from this C point the D has to come anywhere on this projector. So now we have to keep the compass at this particular point and take it the distance up to D 1 keeping the compass at this particular point and taking the distance here okay. So now we are expected so this one we have to bring it this particular point as up to here okay. Now the point is we have to keep the compass at this stage and you take it up to this particular point and draw the arc toward this side. So wherever it will cut this point the projector line which you have drawn previously and that point you have to give as a D dash. So C dash D dash line is representing it as the front view length line C dash D dash is representing as a front view length line this is C dash D dash as a front view length. So as you know the true length of the line is given already in the problem and you know the locus of the point D dash draw a one line here as a locus of this particular point draw a line locus of this point now this is a locus of D point in the front view. So now you measure the 75 millimeter length or take it this distance it is already it is a 75 millimeter keep the compass here and you have to cut it at this particular point. So whenever it is going to cut at this point join that point that becomes as a C dash D dash point C dash D dash point. So this is going to be a true length of the line is concerned. Now he is expected in the problem as draw projection of line C D we have drawn it as a projection of the line in the front view as well as the top view find the angles with HP and VP. So this angle with the HP because it is coming to the this angle is to the xy line above the xy line any angle to the xy line above xy line is an angle made by the line with the HP and similarly so this is the angle made by the line with the VP below the xy line you are going to get it this as an angle this is theta and phi you are expected to write it separately what is those angles are concerned you have to write it separately because that is expected in the problem. Let us you just think it so what are the apparent angles of this problem are concerned what are the apparent angles of this problem. So now apparent angles are as the angle made by front view length with the xy line and angle made by the top view length with the xy line with the xy line. So even if you extend this line up to this one this angle is also same as this angle only because this line and this line are parallel. So now you measure this angle as a alpha that you have to write it as an apparent angle made by the line with the xy line or you can say it as a with the horizontal plane you are going to be writing this as that much the angle you have to write it here. Similarly you measure this angle do not be consider this as a this is a phi angle angle made by the line with the VP and we are expected as angle this angle. So here up to here this angle you are expected here. So this one angle you can write as a beta this is alpha angle and this is beta angle. So now after completion of this particular complete problem you are expected to consider the quality of the work is concerned. So this line has to be there as a dark line this line is to be there as a dark line and this is a medium thickness line. And here this line is a dark line and this is a medium thickness line because this is expected as per the drawing norms. So rest of all the information you are going to be drawing it as all are a construction work. Our expectation is to get this line and this line rest of all the work is a construction work for this particular numerical is concerned. So here once again I will repeat the information as this line the front tube line front tube length line C dash D dash has to be drawn as a dark line and C D line has to be drawn as a dark line and this is medium thickness and this one is a medium thickness and even you are expected as X Y line also to be drawn as a medium thickness. So this is a locus of D thin line and all the projector lines as a thin lines. So you are expected to maintain this quality of work in the problems because the quality also carries a equal importance as far as the numericals are concerned. So now you just after completion of this one you are expected to just relook the problem. Theta angle you have written answer, phi angle you have written answer and your measure this is 75 millimeter this is 75 millimeter so this is what they are given in the problem. Thank you.