Space curve
- Author:
- Bed Prasad Dhakal
A curve C in E3 is the locus of point (x,y,z) whose Cartesian coordinates x,y,z are function of single parameter t. A curve in space in parametric form is given by the equations
x=f(t), y=g(t), z=h(t)
In the parametric form, a space curve s defined as locus of a point whose Cartesian coordinates x,y,z are function of single parameter.
In the parametric form, equation of space curve is given by
......................(1)
The equation given in (1) is called explicit form or parametric form of space curve.
For example,
is a space curve.
१। यसपछिको GeoGebra Applet मा तपाईहरुले parametric equation change गर्न सक्नुहुन्छ । जस्तै,
x=1+t भएको ठाउमा 1-t वा अरु कुनै t को expression लेख्न सक्नुहुन्छ ।
२। Point P=(x,y,z) मा check/un-check गरेर 3D graph मा point लाई locate गर्न सक्नुहुन्छ।
३। Animate point P मा Click गरेर Point P को motion हेर्न सक्नुहुन्छ। र Stop मा Click गरेर Point P को motion
लाई stop गर्न सक्नुहुन्छ।
......................(1)
The equation given in (1) is called explicit form or parametric form of space curve.
For example,
is a space curve.
१। यसपछिको GeoGebra Applet मा तपाईहरुले parametric equation change गर्न सक्नुहुन्छ । जस्तै,
x=1+t भएको ठाउमा 1-t वा अरु कुनै t को expression लेख्न सक्नुहुन्छ ।
२। Point P=(x,y,z) मा check/un-check गरेर 3D graph मा point लाई locate गर्न सक्नुहुन्छ।
३। Animate point P मा Click गरेर Point P को motion हेर्न सक्नुहुन्छ। र Stop मा Click गरेर Point P को motion
लाई stop गर्न सक्नुहुन्छ। Space curve
Which of the following is NOT a space curve?
Given below is a GGB applet. Try different parametric equation given below in this page, and answer the three question at the end of this page. (तल दिएका parametric equation हरु try गर्नुहोस र यस page को अन्तमा दिएको तिनवटा प्रश्नको उतर दिनुहोस ।
Instructions
Input the value of x,y,and z in the applet above. Based on the output, answer the questions given below.
1.
2.
3.
4.
Question 1
Which of the following space curve represent helix? तलका मध्ये कुनचाही space curve ले helix (कलमको spring जस्तो curve) जनाँउदछ?
Question 2
Which of the following space curve represent spiral curve? तलका मध्ये कुनचाही space curve ले spiral (भुरुङ्गको डोरी जस्तो curve) जनाँउदछ?
Question 3
Which of the following space curve represent straight line? तलका मध्ये कुनचाही space curve ले straight line (सिधा रेखा) जनाँउदछ?