In triangle ABC , which of the following is not true: + + = 0 + - = 0 + - = 0 - + = 0

Option c is Correct By law of vectors, + = + = - + + = 0 - + - 0

Vector Algebra — Class 12 Maths Solution

ncert exercise SA NCERT,Page 441,Ex.10.2,Q.No 18

Question

In triangle $ABC$, which of the following is not true:

• $\overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CA} = \vec 0$

• $\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {AC} = \vec 0$

• $\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {CA} = \vec 0$

• $\overrightarrow {AB} - \overrightarrow {CB} + \overrightarrow {CA} = \vec 0$

Step-by-step Solution

{Option c is Correct}

By law of vectors, $\overrightarrow {AB} + \overrightarrow {BC} = \overrightarrow {AC}$
$\Rightarrow \overrightarrow {AB} + \overrightarrow {BC} = - \overrightarrow {CA}$

$\Rightarrow \overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CA} = \vec 0 - \Rightarrow \overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {CA} \ne \vec 0$

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