Write the value of ( i j ). k + ( j + k ). j - Vidyadip

Question

Write the value of $\big(\hat{\text{i}}\times\hat{\text{j}}\big).\hat{\text{k}}+\big(\hat{\text{j}}+\hat{\text{k}}\big).\hat{\text{j}}$

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Answer

$\big(\hat{\text{i}}\times\hat{\text{j}}\big).\hat{\text{k}}+\big(\hat{\text{j}}+\hat{\text{k}}\big).\hat{\text{j}}$
$=\hat{\text{k}}.\hat{\text{k}}+\hat{\text{j}}.\hat{\text{j}}+\hat{\text{k}}.\hat{\text{j}}$ $\big(\because\hat{\text{i}}\times\hat{\text{j}}=\hat{\text{k}}\big)$
$=|\hat{\text{k}}|^2+|\hat{\text{j}}|^2+0$ $\big(\because\hat{\text{k}}.\hat{\text{j}}=0\big)$
$=1^2+1^2$
$=2$

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