CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A(a), B(b), C(c) are the vertices of a triangle ABC and R(r) is any point in the plane of triangle ABC, then r.(a×b+b×c+c×a) is always equal to



Your Answer
A

Zero

Correct Answer
B

[a b c] 

Your Answer
C

[ a b c] 

Your Answer
D

None of these


Solution

The correct option is B

[a b c] 


A vector perpendicular to the plane of A(a), B(b), C(c) is (ba)×(ca)=a×b+b×c+c×a
Now  for any point R(r) in the plane of A, B, C
(ra).(a×b+b×c+c×a)=0r.(a×b+b×c+c×a)a.(a×b+b×c+c×a)=0r.(a×b+b×c+c×a)=0+a.b×c+0r.(a×b+b×c+c×a)=[a b c]

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image