How the problems are made
Each problem is built in 3D from whole-number data, as a question paper gives it, and every answer comes from exact geometry. The key is drawn full size by the rotating-line method: projectors, true lengths at θ and φ, loci, arcs, α, β and the traces, with an exact check for each answer. Printed at 100%, you can lay your sheet over the key.
The six levels
- Points in the four quadrants: draw them, or read them from the views.
- Lines parallel or perpendicular to a plane, or inclined to one plane.
- A line inclined to both planes: view lengths, α, β, projector distance.
- The reverse: true length, θ and φ from the views or end positions.
- Traces (HT and VT), and lines in a profile plane.
- Lines in the other quadrants, across quadrants, and lying in the HP or VP.
An example from set ABCDEF
Line PQ, 95 mm long, is inclined at 20° to the HP and 45° to the VP, with P 30 mm above the HP and 20 mm in front of the VP. Full size, p′q′ is 67.2 mm (95 × cos 45°) and pq 89.3 mm (95 × cos 20°). The end projectors are 58.8 mm apart, α is 28.9° and β 48.8°, both larger than the true angles. Open set ABCDEF
Questions
How do you find the true length of a line in engineering drawing?
Turn the top view ab about a until it is parallel to XY, at ab₁, and project b₁ to the locus of b′: a′b₁′ is the true length, at θ to XY. Turning a′b′ about a′ to a′b₂′ instead gives ab₂, the true length at φ.
What is the difference between θ and α?
θ is the true angle between the line and the HP. α is the angle its front view a′b′ makes with XY. For a line inclined to both planes α is always larger than θ, and β larger than φ.
What are the HT and VT of a line?
The horizontal trace (HT) is where the line, produced if needed, meets the HP; the vertical trace (VT) is where it meets the VP. Produce a′b′ to meet XY at h′ and project to ab produced: that is h, the HT. The VT comes the same way from ab.
How do you tell which quadrant a point is in?
Look at both views. Front view above XY and top view below: first quadrant. Both above: second. Front view below and top view above: third. Both below: fourth. A view on XY means the point lies in that plane.
Is this first-angle or third-angle projection?
First angle, the method BIS SP 46 sets for Indian drawing practice and the one the KTU, Mumbai and GTU syllabi use. The front view is above XY and the top view below it for a point in front of the VP and above the HP.
How accurate does my drawing need to be?
Lengths within 1 mm and angles within 1° of the value in the key count as right, which is what a sharp pencil gives at full size. The key shows each answer to 0.1 with its exact working.
How do I use this with a class?
Share with class sends a link to the same problems. To stop copying, print a class set: each student gets a different set with full-size drawing spaces, and the keys follow, labelled by copy number.
Conventions checked 26 October 2026: NPTEL Engineering Drawing, lectures 17 to 21; IIT Guwahati ME 111 (PDF); NITK Virtual Lab; syllabi of KTU, Mumbai FEC204 and GTU (PDFs).