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  • Show that the vectors <img alt="2 \widehat{i} - \widehat{j} + \widehat{k} , 3 \widehat{i} + 7 \widehat{j} + \widehat{k}" src="https://learn.careers360.com/latex-image/?2%20%5Cwidehat%7Bi%7D%20-%20%5Cwidehat%7Bj%7D%20&plus;%20%5Cwidehat%7Bk%7D%20%2C

Show that the vectors 2 \widehat{i} - \widehat{j} + \widehat{k} , 3 \widehat{i} + 7 \widehat{j} + \widehat{k} and 5 \widehat{i} + 6 \widehat{j} + 2 \widehat{k} form the sides of a right-angled triangle.

 

 
 
 
 
 

Answers (1)

$\overrightarrow{{a}}=2 \hat{{i}}-\hat{{j}}+\hat{{k}}

\overrightarrow{{b}}=3 \hat{{i}}+7 \hat{{j}}+\hat{{k}}$

\overrightarrow{c}=5 \hat{{i}}+6 \hat{j}+2 \hat{k}

\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}} \Rightarrow $ These three vectors form a triangle $

\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=6 -7+1 = 0

\Rightarrow \overrightarrow{\mathrm{a}} \perp \overrightarrow{\mathrm{b}}

Hence these three vectors form the right angle triangle.

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Safeer PP

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