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In a triangle $\mathrm{ABC}$, if taken in order, consider the following statements:
$1.$ $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CA}}=\overrightarrow{0}$
$2.$ $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}-\overrightarrow{\mathrm{CA}}=\overrightarrow{0}$
$3.$ $\overrightarrow{\mathrm{AB}}-\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CA}}=\overrightarrow{0}$
$4.$ $\overrightarrow{\mathrm{BA}}-\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CA}}=\overrightarrow{0}$
How many of the above statements are correct?
Options:
$1.$ $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CA}}=\overrightarrow{0}$
$2.$ $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}-\overrightarrow{\mathrm{CA}}=\overrightarrow{0}$
$3.$ $\overrightarrow{\mathrm{AB}}-\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CA}}=\overrightarrow{0}$
$4.$ $\overrightarrow{\mathrm{BA}}-\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CA}}=\overrightarrow{0}$
How many of the above statements are correct?
Solution:
2143 Upvotes
Verified Answer
The correct answer is:
One
From triangle law of vector addition
$\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CA}}=0$
Only statement $(1)$ is correct.
$\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CA}}=0$
Only statement $(1)$ is correct.
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