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Let \vec{r }=\hat{i}-\hat{k},  \vec{a}=\hat{i}-\hat{j}+\hat{k},\: \: \vec{b}=2\hat{i}-3\hat{j}+4\hat{k} then which of the following linear combinations of \vec{a}\, \, and\, \, \vec{b} equal \vec{r}

Option: 1

\vec{r}=3\vec{a}-\vec{b}


Option: 2

\vec{r }=3\vec{a}+\vec{b}


Option: 3

\vec{r}=7\vec{a}-3\vec{b}


Option: 4

\vec{r }=\vec{b}-\vec{a}


Answers (1)

best_answer

\\3\vec{a}-\vec{b}=3(\hat{i}-\hat{j}+\hat{k})-(2\hat{i}-3\hat{j}+4\hat{k})=\hat{i}-\hat{k}=\vec{r }\, \, \, \, \, \, \, \, \, \\\therefore option(A)

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manish

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