Question

In triangle ABC which of the following is not true: A. B. C. D.

Answer 1

In the given ΔABC, AC → is the resultant of AB → and BC → . So,

AC → = AB → + BC → AB → + BC → − AC → =0 (1)

For option (A),

AB → + BC → + CA → =0(2)

But, CA → =− AC → so, equation (2) become,

AB → + BC → − AC → =0

This equation is same as equation (1).

Thus, option (A) is true.

For option (B),

AB → + BC → − AC → =0

Same as equation (1),

Thus, option (B) is true.

For option (C),

AB → + BC → − CA → =0(3)

But, CA → =− AC → so, equation (3) become,

AB → + BC → + AC → =0

This equation is not same as equation (1),

Thus, option (C) is not true.

For option (D),

AB → − CB → + CA → =0(4)

But, CA → =− AC → and CB → =− BC → so, equation (4) becomes,

AB → + BC → − AC → =0

This equation is same as equation (1),

Thus, option (D) is true.

Hence, the correct answer is (C).