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Home / Doubts and Solutions/JEE/Mathematics

Q)the points (0,-1,-1) , (-4 ,4,4) , (4,5,1) , & (3,9,4) are
(A) collinear    (B) Coplanar    (C) forming a square.

Asked by araima2001 14th September 2017, 3:37 AM
Answered by Expert
Answer:
begin mathsize 16px style Let space straight A space equals open parentheses 0 comma negative 1 comma negative 1 close parentheses comma space straight B space equals open parentheses negative 4 comma space 4 comma space 4 close parentheses comma space straight C space equals open parentheses 4 comma space 5 comma space 1 close parentheses space and space straight D space equals space open parentheses 3 comma space 9 comma space 4 close parentheses Here space AB space equals space open parentheses negative 4 comma space 5 comma space 5 close parentheses AC space equals space open parentheses 4 comma space 6 comma space 2 close parentheses AD space equals space open parentheses 3 comma space 10 comma space 5 close parentheses We space can space see space that space points space are space non minus collinear. Now space we space will space check space its space determinant. open vertical bar table row cell negative 4 end cell 5 5 row 4 6 2 row 3 10 5 end table close vertical bar equals negative 4 open parentheses 30 minus 20 close parentheses minus 5 open parentheses 20 minus 6 close parentheses plus 5 open parentheses 40 minus 18 close parentheses space equals space 0 Hence space given space points space are space coplanar. end style
Answered by Expert 14th September 2017, 9:18 AM
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