 Today we are going to study the projection of lines, myself Mr. S. P. Mankani, assistant professor, department of mechanical engineering, Valchian Institute of Technology, Solapur. So at the end of this lecture, students will be able to solve problems of projection of lines inclined to HP and VP of a plane, line inclined to both HP and VP. So here the problem we are going to read properly first, line AB is 75mm long and it is 30 degree and 40 degree line inclined to HP and VP respectively. So here the given condition is line is having a length of 75mm long and it is making an angle of 30 degree and 40 degree, irrespective as with HP and VP means first 30 degree angle is making with HP and second 40 degree angle is making with VP. And A is 12mm above the horizontal plane and 10mm in front of the vertical plane. So draw the projection of line in the first quadrant. There is no need to give every time as a first quadrant, second quadrant, third quadrant. We are going to deal in our lectures purely related with the first quadrant only. So based on this one, first before starting any problem you are expected to draw the xy line first. Give the naming as x and y. We are going with this problem as in retail. So here you are going to write it the vertical line for measurement purpose. So here the length is given as A point, A is situated here as well as here because it comes in the front view as well as in the top view. The position of A is given as 12mm above the horizontal reference plane. So this xy line itself we are going to be considering it as a horizontal reference plane as well as vertical reference plane. Any measurement above the xy line is indicating it as the distance from horizontal reference plane. So here it is given as 12mm. And A is 12mm above the horizontal reference plane. So keep the scale here and measure as a 12mm in the above direction and so wherever that position comes that point you are going to be locating it as a A dash. All the notation you are going to be using in the front view as with a dash mark. This point is A dash mark and this distance is 12mm. This is 12mm distance. So then you have to come for the next point. This you are representing it as a A dash point and then you come for the A point. So here it is a end A is 10mm in front of the vertical reference plane he has given. So 10mm you measure the distance of 10mm from the xy line that too below the xy line. This is the 10mm from the xy line below the xy line which you have discussed in the previous lectures as far as how to measure the distance above the horizontal plane and as well as in front of the vertical plane related in the first angle projection. Now you got as a position of A in the front view and position of A in the top view. So this with the reference of this point you are going to be locating as a 75mm length that is the true length of line AB. You are located only A now you are going to be thinking of the B point. For that he has given the reference as 30 degree and 40 degree angle. 30 degree angle it is making with the horizontal reference plane and 40 degree angle it is making with the vertical reference plane. So as I explained as you can take the angle in this direction or in this direction. So here you are located as a point A dash here and you do not have space this side you are going with the angle as toward this side only you are not supposed to go for this side because the space is not available in this direction. Even if you are going to take it this in this direction also you can take it okay. So as he has given as a 75 degree angle to the horizontal reference plane. This line is it is length is infinite length. So anyway you can continue this line as far as our requirement is concerned. Now with this particularly the line you are going to take the reference as this point and 75 degree angle sorry this is 75 length and 30 degree as an angle. So here also you are drawn a one reference line and this is also one reference line. Both the lines are parallel to the XY line. So that indicating as this as a reference horizontal reference plane and this is a vertical reference plane because it is parallel to the XY line. So now you are drawn this line. First you have to draw the line by locating as a 30 degree angle with this particular point and with this reference. So this angle is a 30 degree angle just you are drawn a one line. And that line you have to cut it as a 75 millimeter is given as 75 millimeter okay keep the scale here and take it 75 millimeter wherever it will come. So that point you have to locate it as the true length. This is a true length because it is a 75 millimeter he has given and this is a theta angle given as 30 degree angle. And here it is a b1 dash point. So this length a dash b1 dash is a true length a dash b1 dash is a true length okay. This is actually given length and given angle true inclination and true length. So now we are going with the top view keeping this a as a position and you are going to take it as a this as an angle this angle is nothing but you are going to be representing as a phi angle phi angle is given in this as 40 degree angle keep the protector here take it 40 degree angle and locate the point and join that point with the a point and this line you are going to get it as a this length is also a 75 millimeter given true length. Because this angle as well as this angle you are going to be taking it as a true inclination. This is an angle made by the line with the vertical reference plane you are going to measure below the xy line to the xy line if you are extending this line up to this one it will become as a the given angle as 40 degree here also you can locate it. So now this is 40 degree line you are drawn and locate it as a phi angle theta and phi angles are true inclinations join this point a point with this line and this is a b1 point you are expected to draw a one locus point at this b1 b1 dash and one locus point at b1. So these locus points they are going to write this as a locus line at this point as well as locus line means whatever the front you are going to be representing means whatever the front you are going to write that point has to come anywhere on this line anywhere on this locus line. Similarly the top line anywhere on this line means you are going to join that top line from this particular point to this one the point is coming anywhere on this locus line. So now we are going with the next step. So either you can bring this point in the downward direction or you can bring this point in the upward direction anywhere. You can start either from this direction or from this direction. Now you are going to bring this point in the upper direction. So here A1 dash and this particular point. A1 dash and this particular point is going to be given as a front tube length of a given line. Front tube length of a given line means when the line is going to be tilted as a 30 degree to the HP and 40 degree to the VP it looks in this way whatever the position you are going to get it in the next step. So keep compass here, take it this much distance and draw the arc in this direction. Keep the compass here, take it this distance, draw the arc towards this direction. So wherever it will cut the locus of B point you are going to locate that point as a B dash point. So now you are tilted this one in the upper direction. So join this A dash point with this particular point as a B dash point. This is B dash point. Join this line with a dark line. This line with a dark line. So now this is nothing but a front tube line. Means exactly line looks in the front tube in this way. If you are going to tilt the given line of a 75 millimeter length at a 12 millimeter above the horizontal plane tell millimeter below the vertical in front of the vertical reference plane and that too as a theta degree this theta degree is nothing but a 30 degree and 40 degree that time it looks in this way. So now you bring this point directly towards in the downward direction it will cut anywhere on this locus point otherwise you can bring this line in the downward direction then same procedure you have to order for the top view also. So directly you can get it as a this line bringing it in the downward direction it will cut on the locus point. So now you are going to get it this as A B as a top view length. A B as a top view length. So here you are expected to draw the line all the construction work should be drawn as a thin line. And here you are going to draw this as a A dash B 1 dash as a true length it is a medium thickness A and B 1 as a true length it is a medium thickness. And this is A dash and B dash as a front view length this should be drawn as a dark line this front view length as well as top view length you are expected to draw as a dark line because you are expected as a this is a final required projection. And as far as rest of all the lines is a construction line rest of all the lines are the construction lines that has to be drawn as a thin line. So now this concludes the problem. So here this is a solution for the given problem. In the same base I am going to give one more problem in the next step just to think it about that particularly problem. A line A B 50 millimeter long is inclined to HP as 30 degree and to VP as 45 degree angles just changed the second angle is changed. The point A is 10 20 millimeter above the horizontal plane and 35 millimeter in front of the vertical reference plane draw the projection of the line. So now my question is you are initially are going to draw the xy line xy line where this particularly 20 millimeter comes and where this 35 millimeter comes 20 millimeter comes above the horizontal reference plane and 35 millimeter comes below the xy line thank you.