For any vector r - r - - i - 2- r - j - 2- r - k - 2-

Let #160;r #8594;=r1i^+r2j^+r3k^r #8594; #183;i^2+r #8594; #183;j^2+r #8594; #183;k^2=r12+r22+r32 #160; #160; #160; #160; #160; #160 ...

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Linear Combination of Vectors

For any vecto...

Question

For any vector $\vec{r}, {(\vec{r} . \hat{i})}^{2} + {(\vec{r} . \hat{j})}^{2} + {(\vec{r} . \hat{k})}^{2}$ = ________________ .

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\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 =___________________.

¯ ¯ ¯ r

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

i, j, k

a

a \times r = ˆ j,

a . r

a

r

{| a \times r |}^{2} + {| a . r |}^{2} = {| a |}^{2} {| r |}^{2}

\vec{r},

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

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

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