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  • Let <img alt="\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}+\hat{j}+\hat{k} \text { and } \vec{c}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cvec%7Ba%7D%3D%5Chat%7Bi%7D-2%2

Let \vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}+\hat{j}+\hat{k} \text { and } \vec{c} be a vector such that \vec{a}+(\vec{b} \times \vec{c})=\overrightarrow{0} and \vec{b} \cdot \vec{c}=5 . Then, the value of 3(\vec{c} \cdot \vec{a}) is equal to ________.

Option: 1

0


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\vec{\mathrm{a}}+(\vec{\mathrm{b}} \times \vec{\mathrm{c}})=\overrightarrow{0} \\

\Rightarrow \vec{\mathrm{b}} \times \vec{\mathrm{c}}=-\vec{\mathrm{a}} \\

\Rightarrow \vec{\mathrm{a}}\perp \vec{\mathrm{c}} \\

\Rightarrow \vec{\mathrm{a}} \cdot \vec{\mathrm{c}}=0 \\

\Rightarrow 3(\vec{\mathrm{a}} \cdot \vec{\mathrm{c}})=0

Hence answer is 0

Posted by

vishal kumar

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