If a+b=i and a=2 i-2 j+2 k, then |b| equals: - Vidyadip

Question

If $\vec{a}+\vec{b}=\hat{i}$ and $\vec{a}=2 \hat{i}-2 \hat{j}+2 \hat{k}$, then $|\vec{b}|$ equals:

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Answer

$\text {Given, } \hat{a}+\hat{b}=\hat{i} \text { and } \vec{a}=2 \hat{i}-2 \hat{j}+2 \hat{k}$
$\Rightarrow 2 \hat{i}-2 \hat{j}+2 \hat{k}+\vec{b}=\hat{i} \Rightarrow \vec{b}=\hat{i}-(2 \hat{i}-2 \hat{j}+2 \hat{k})$
$\Rightarrow -\hat{i}+2 \hat{j}-2 \hat{k}$
$\therefore |\vec{b}|=\sqrt{(-1)^2+(2)^2+(-2)^2}$
$=\sqrt{1+4+4}=\sqrt{9}=3$

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