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The plane ax+by+cz=1 meets the co-ordinate axes in A,B and C. The centroid of the triangle is- (3a,3b,3c) (a/3, b/3, c/3) (3/a, 3/b, 3/c) (1/3a, 1/3b, 1/3c) What i am not understanding is how the x,y,and z intercepts are equal to a , b and c respectively.

The plane ax+by+cz=1 meets the co-ordinate axes in A,B and C. The centroid of the triangle is-
  1.  (3a,3b,3c)
  1.  (a/3, b/3, c/3)
  2. (3/a, 3/b, 3/c)
  3. (1/3a, 1/3b, 1/3c)    
What i am not understanding is how the x,y,and z intercepts are equal to a , b and c respectively. 
 

Grade:11

1 Answers

Yash Jain
55 Points
7 years ago
The correct answer is (D).
First of all, it should be clear that a,b,c are not the intercepts of the axes x,y,z resp. If that is true then (a,0,0), (0,b,0) and (0,0,c) should satisfy the eq of the plane, which is not the case. 
The intercepts that the plane make on the axes is 1/a,1/b,1/c (you can verify by points these points or just converting the given eq in the intercept form). So A,B,C are resp. (1/a,0,0),(0,1/b,0),(0,0,1/c).
Thus, the co-ordinates of the centroid is (1/3a,1/3b.1/3c).
Hence the correct option is (D)

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