Projections of Planes Questions and Answers

Answer: C

Correct answer: 1-Q, 2-P, 3-R

Three attitudes with three characteristic appearances. A figure parallel to the horizontal plane gives its true shape in the plan, since it is not foreshortened there. One perpendicular to the horizontal plane is seen edge on from above and appears as a line in the plan. And one inclined to both planes is foreshortened in both views and shows its true shape in neither.

Answer: D

Correct answer: 1-Q, 2-P, 3-R

Three techniques with three distinct effects. Change of position moves the figure until it is parallel to a principal plane, where its true shape appears. An auxiliary plane parallel to the figure gives the true shape directly, without moving anything. And an auxiliary plane perpendicular to the figure shows it as a line, which is the intermediate step that makes the parallel auxiliary possible.

Answer: A

Correct answer: 2, 4, 1, 3

Begin with the plan and elevation as given. Project a first auxiliary on a plane perpendicular to the figure, in which it appears as a straight line - this establishes its attitude. Project a second auxiliary parallel to that line, and therefore parallel to the figure, which shows the true shape. Only then can the dimensions be measured from it.

Answer: B

Correct answer: 1 and 2 only are correct

Statements 1 and 2 are correct: the traces meet on the reference line, and an inclined circle projects as an ellipse. Statement 3 has the traces the wrong way round - a plane parallel to the horizontal plane has no horizontal trace, since it never meets that plane, and its vertical trace is the line parallel to the reference line.

Answer: C

Correct answer: a plane parallel to the vertical plane

The elevation is the projection onto the vertical plane, so a figure appears there in true shape when it is parallel to that plane. A figure parallel to the horizontal plane gives its true shape in the plan instead, and one inclined or perpendicular to both gives it in neither principal view.

Answer: D

Correct answer: it is inclined to both principal planes

A profile plane is perpendicular to both principal planes, not inclined to them; being inclined to both is the description of an oblique plane. The other three statements all follow from that perpendicularity: the traces are at right angles to the reference line, and a figure in the plane appears edge on in both principal views.

Answer: A

Correct answer: too small

The plan of an inclined figure is its true area multiplied by the cosine of the inclination, and a cosine is never greater than one, so the plan always understates the area. The error grows with the tilt, reaching half at sixty degrees and vanishing only when the figure is parallel to the plane of projection.

Answer: B

Correct answer: perpendicular to the horizontal plane and inclined to the vertical

Appearing as a line in the plan means the figure is seen edge on from above, so it is perpendicular to the horizontal plane. Appearing foreshortened rather than in true shape in the elevation means it is not parallel to the vertical plane either, so it must be inclined to it - which is exactly the combination described.

Answer: C

Correct answer: both the assertion and the reason are true and the reason explains the assertion

Both are true and the reason gives the mechanism precisely. Tilting shortens dimensions measured across the axis of tilt by the cosine of the angle and leaves those along it untouched, so the circle’s diameters are affected unequally and the figure becomes an ellipse - with the true diameter as the major axis and its foreshortened counterpart as the minor.

Answer: D

Correct answer: the assertion is false although the reason offered is a true statement in itself

The reason is true - an auxiliary plane parallel to the figure does give the true shape - but that plane cannot be set up in one step. Its direction depends on knowing the figure’s attitude, which is established by a first auxiliary in which the figure appears as a line. Two successive projections are therefore needed, not one.