If vec{a} = 4hat{i} + hat{j} + hat{k}, vec{b} | vedclass

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(C) Step $1$: Calculate $(\vec{a} + \vec{b}) = (4\hat{i} + \hat{j} + \hat{k}) + (2\hat{i} + \hat{j} + 2\hat{k}) = 6\hat{i} + 2\hat{j} + 3\hat{k}$.Step

Vedclass · Accepted Answer

$61$

Vedclass · Answer

(C) Step $1$: Calculate $(\vec{a} + \vec{b}) = (4\hat{i} + \hat{j} + \hat{k}) + (2\hat{i} + \hat{j} + 2\hat{k}) = 6\hat{i} + 2\hat{j} + 3\hat{k}$.Step $2$: Calculate $(\vec{b} + \vec{c}) = (2\hat{i} + \hat{j} + 2\hat{k}) + (3\hat{i} + 4\hat{j} + 5\hat{k}) = 5\hat{i} + 5\hat{j} + 7\hat{k}$.Step $3$: Calculate the dot product $(\vec{a} + \vec{b}) \cdot (\vec{b} + \vec{c}) = (6\hat{i} + 2\hat{j} + 3\hat{k}) \cdot (5\hat{i} + 5\hat{j} + 7\hat{k})$.Step $4$: Perform the scalar multiplication: $(6 	imes 5) + (2 	imes 5) + (3 	imes 7) = 30 + 10 + 21 = 61$.

If $\vec{a} = 4\hat{i} + \hat{j} + \hat{k}$, $\vec{b} = 2\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{c} = 3\hat{i} + 4\hat{j} + 5\hat{k}$, then $(\vec{a} + \vec{b}) \cdot (\vec{b} + \vec{c}) =$

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