# An exam question testing your spatial sense. (Is it worded correctly?)

I recently got the following question from a friend. This kind of question was asked in one of her exams (it really doesn't matter what kind of exam that was). I after trying to solve said question think that something is profoundly wrong about the wording in it and in turn the provided answers. First of all, here is the question:

You are a skydiver and jump out of an airplane. you lie horizontally in the air and look down. to the north of you is a city, above you the plane, to the left of you/in the west is the sun, in the east there is a mountain, below you the ground and in the south there is a sea.

you rotate 90 degrees clockwise around your longitudinal axis.

1. What is behind you now? {a: plane, b: city, c: sun, d: mountain, e: sea, f: ground}

you rotate 90 degrees counterclockwise around your transverse axis.

1. what is now to your right? {a: plane, b: city, c: sun, d: mountain, e: sea, f: ground}

you rotate 180 degrees around your longitudinal axis and 180 degrees around your transverse axis.

1. what is now to your right? {a: plane, b: city, c: sun, d: mountain, e: sea, f: ground}

you rotate counterclockwise around your longitudinal axis by 270 degrees.

1. What is on your left? {a: plane, b: city, c: sun, d: mountain, e: sea, f: ground}

To clarify further: the instructions are done in sequence, meaning for question 3 for example instructions 1, 2 and 3 are done in sequence, then question 3 is asked.

The bold ones are the correct answers.

Now, my questions are the following:

1. If I am not incorrect they assume that the transverse axis does not rotate with the person when the person is rotated along their longitudinal axis. Isn't that just wrong?

2. Don't they also assume that one looks from the right onto the transverse axis and then rotate clockwise/counterclockwise. Couldn't one look from the left which would result in clockwise/counterclockwise being interchanged?

3. Aren't (if my first two points are valid) the given answers totally wrong?

That's why I think this question is very, very poorly (and wrongly) worded. Am I right about my train of thought or am I missing something?

If anyone is interested: this question was originally asked in German, I hope my translation is 100% correct. For reference, the German version, uncapitalised:

sie sind ein fallschirmspringer und springen aus einem flugzeug. sie liegen horizontal in der luft und schauen nach unten. nördlich von ihnen befindet sich eine stadt, über ihnen das flugzeug, links von ihnen beziehungsweise im westen befindet sich die sonne, im osten befindet sich ein berg, unter ihnen der boden und im süden erstreckt sich ein meer.

sie drehen sich um 90 grad im uhrzeigersinn um ihre längsachse.

1. was befindet sich nun hinter ihnen? {a: flugzeug, b: stadt, c: sonne, d: berg, e: meer, f: boden}

sie drehen sich um 90 grad gegen den uhrzeigersinn um ihre querachse.

1. was befindet sich nun rechts von ihnen? {a: flugzeug, b: stadt, c: sonne, d: berg, e: meer, f: boden}

sie drehen sich um 180 grad um ihre längsachse und um 180 grad um ihre querachse.

1. was befindet sich nun rechts von ihnen? {a: flugzeug, b: stadt, c: sonne, d: berg, e: meer, f: boden}

nun drehen sie sich um 270 grad gegen den uhrzeigersinn um ihre längsachse.

1. was befindet sich nun links von ihnen? {a: flugzeug, b: stadt, c: sonne, d: berg, e: meer, f: boden}
• I think it's unclear, even the first step. "clockwise" looking from the top of your head, or "clockwise" looking from your feet? When I think of myself rotating clockwise about my longitudinal axis, I imagine bringing my left arm across my front, and my right elbow backward, so that's clockwise looking at the top of my head. Their answer seems to be clockwise looking at the bottoms of your feet. Jul 2, 2020 at 2:19
• The second step is also unclear. Is your transverse axis the one from side to side that you would rotate around if you did a somersault, or the one from front to back that you would rotate around if you did a cartwheel? Jul 2, 2020 at 2:55
• Yes you are right! Jul 2, 2020 at 6:08

I think the questions and answers are essentially correct as written. I don't speak German, so I can't say whether or not the German words are used correctly, but if I make some reasonable assumptions about what everything means, then I get the marked answers.

(By the way, you seem to have a translation error in the last one; the German says "gegen den uhrzeigersinn" but you wrote "clockwise".)

The meanings of the German phrases are apparently:

• gegen den Uhrzeigersinn um ihre Längsachse – counterclockwise about your longitudinal axis, or "roll left".
• gegen den Uhrzeigersinn um ihre Querachse – counterclockwise about your sagittal axis, or "yaw left".

So we have:

Initially: Head - city, feet - sea, left arm - sun, right arm - mountain, back - airplane, belly - ground.

Roll right: Head - city, feet - sea, left arm - airplane, right arm - ground, back - mountain, belly - sun.

Yaw left: Head - airplane, feet - ground, left arm - sea, right arm - city, back - mountain, belly - sun.

Roll 180: Head - airplane, feet - ground, left arm - city, right arm - sea, back - sun, belly - mountain.

Yaw 180: Head - ground, feet - airplane, left arm - sea, right arm - city, back - sun, belly - mountain.

Roll right (by rolling left by 270): Head - ground, feet - airplane, left arm - sun, right arm - mountain, back - city, belly - sea.

• Yes you are right, I wrote clockwise instead of counterclockwise. Jul 2, 2020 at 5:55
• But isn't that wrong as the transverse axis rotates with me when I rotate along my longitudinal axis? Jul 2, 2020 at 5:58
• It would also be great if you could add the "reasonable assumptions" you made. Jul 2, 2020 at 6:03
• Ah, I understand what you are doing. You are rotating along the vertical axis (yaw left/right). What you need to do is rotate along the transverse axis (pitch left/right). Hope that helps! Jul 2, 2020 at 6:11
• The instructions and answers look correct to me, assuming longitudinal axis is head-to-feet and transverse is back-to-front. It is a bit ambiguous what "clockwise" means though. If you are lying on the back and turn clockwise, which way should it be? Jul 3, 2020 at 9:03