I teach first year uni students and they don't seem to know what is a plane(adsbygoogle = window.adsbygoogle || []).push({});

and what is a line in 3d. I have been paid to make an online multiple choice

a prototype is given below. Any help would be appreciated

1)x+y=5

(a) has infinite solutions

examples of solutions are (-1,6), (0,5) , (1,4),(2,3) etc

(b) has a unique solution

2) x+y=0 could be represented by the parametric equation

(a) (0,5) + (-1,1)t

where t can take any value

(b) (0,5) + (1,1)t

where t can take any value

3) x+y =5 can be represented by

(1 1 |5)

4) x+y=5

(a) is a line

(b) is a plane

5) x+y+z=5

(a) Has infinite solutions

examples of solutions are (-1,0,6), (0,-1,6), (0,0,5),(1,0,4)

(b) Has a unique solution

6) x+y+z=5 could be represented by the parametric equation

(a) (5,0,0)+(-1,1,0)s + (-1,0,1)t

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# How do you explain x+y+z=5 is a plane?

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