Find a . b when a = j +2 k and b =2 i + k - Vidyadip

Question

Find $\vec{\text{a}}.\vec{\text{b}}$ when
$\vec{\text{a}}=\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{k}}$

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Answer

$\vec{\text{a}}.\vec{\text{b}}=(\hat{\text{j}}+2\hat{\text{k}}).(2\hat{\text{i}}+\hat{\text{k}})$
$=(0\times\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}})(2\hat{\text{i}}+0\times\hat{\text{j}}+\hat{\text{k}})$
$=(0)(2)+(1)(0)+(2)(1)$
$=0+0+2$
$\vec{\text{a}}.\vec{\text{b}}=2$

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