In the given triangle $A B C$ which of the following is not true
A. $- - \to A B + - - \to B C + - - \to C A = \to 0$
B. $- - \to A B + - - \to B C - - - \to A C = \to 0$
C. $- - \to A B + - - \to B C + - - \to A C = \to 0$
D. $- - \to A B - - - \to C B + - - \to C A = \to 0$

Open in App

Solution

It is given that in $Δ A B C, - - \to A C$ is the resulatant of $- - \to A B$ and $- - \to B C$
$- - \to A B + - - \to B C = - - \to A C$
$- - \to A B + - - \to B C - - - \to A C = \to 0$
Hence, (B) is true.
Now, $- - \to A B + - - \to B C + - - \to C A = \to 0$
$∵ - - \to A C = - - - \to C A$
Hence, (A) is true and therefore (C) is not true.
Now, as $- - \to A B + - - \to B C + - - \to C A = \to 0$
$\Rightarrow - - \to A B - - - \to C B + - - \to C A = \to 0$
Hence, (D) is true

Final answer:
Hence, the option (C) is not true.

Suggest Corrections

Similar questions

\vec{A B} + \vec{B C} + \vec{C A} = \vec{0}

\vec{A B} + \vec{B C} - \vec{A C} = \vec{0}

\vec{A B} + \vec{B C} - \vec{C A} = \vec{0}

\vec{A B} - \vec{C B} + \vec{C A} = \vec{0}

Question 60

In the given figure?

a) is AC + CB = AB?

b) is AB + AC = CB?

c) is AB + BC = CA?

In Triangle ABC, which of the following is not true:

(a) AB + BC + CA = 0
(b) AB + BC - AC = 0
(c) AB + BC - CA = 0
(d) AB - CB + CA = 0

(a b + b c) (a b - b c) + (b c + c a) (b c - a c) + (c a + a b) (a c - a b)

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program