CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

ABCD is a regular tetrahedron. M(0,0,0) is the midpoint of the altitude DN of the tetrahedron. Coordinates of the points A and B are (0,0,2) and (b,b,0) respectively (with b>0). Also x - coordinate of the point C is given to be positive. Then which of the following is/are correct?


Correct Answer
A
Image of point D in the plane generated by ABC is (22,0,2)
Your Answer
B
Image of point D in the plane generated by ABC is (2,0,22)
Your Answer
C
Volume of tetrahedron ACBM is 423
Correct Answer
D
Volume of tetrahedron ACBM is 43

Solution

The correct options are
A Image of point D in the plane generated by ABC is (22,0,2)
D Volume of tetrahedron ACBM is 43
AB=BC=CD=AD=a

a=22
MA=MB=MC=2    (Using symmetry)
MB=22b2=4b=2
B(2,2,0)
MA2+MB2=AB2MAMB
Similarly MAMC,MBMC
MA.MC2z=0MB.MC2x+2y=0y=x & z=0 C(x,x,0)
Also MC2=2x2=MA2=4x=2  (x>0)
So C(2,2,0)
Coordinates of N are (223,0,23) and hence D is (223,0,23).DN is normal to the plane ABC. N is mid point of DD so D=(22,0,2)
Since MA,MB,MC are orthogonal triads
Volume of tetrahedron is= 16|MA|.|MB|.|MC|=43.

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image