For any non-zero vectors r - the expression r - - i - i - r - - j - j - r - - k - k - equals

Let #160;r #8594;=r1i^+r2j^+r3k^r #8594; #183;i^i^+r #8594; #183;j^j^+r #8594; #183;k^k^=r1i^+r2j^+r3k^ #160; #160; #160; #160; #160; ...

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Exponents

For any non-z...

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For any non-zero vectors $\vec{r},$ the expression $(\vec{r} . \hat{i}) \hat{i} + (\vec{r} . \hat{j}) \hat{j} + (\vec{r} . \hat{k}) \hat{k}$ equals ___________.

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¯ ¯ ¯ r

¯ i \times (¯ ¯ ¯ r \times ¯ i) + ¯ j \times (¯ ¯ ¯ r \times ¯ j) + ¯ ¯ ¯ k \times (¯ ¯ ¯ r \times ¯ ¯ ¯ k) =

\vec{r}, {|\vec{r} \times \hat{i}|}^{2} + {|\vec{r} \times \hat{j}|}^{2} + {|\vec{r} \times \hat{k}|}^{2} = λ {|\vec{r}|}^{2}, then λ =___________________.

\vec{r}, {(\vec{r} . \hat{i})}^{2} + {(\vec{r} . \hat{j})}^{2} + {(\vec{r} . \hat{k})}^{2}

\to r

(\to r \times^i) \times^i + (\to r \times^j) \times^j + (\to r \times^k) \times^k =

\to r, | \to r \times^I |^{2} + | \to r \times^j |^{2} + | \to r \times^k |^{2}

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