Let a→=i^+2j^-3k^ and b→=2i^-3j^+5k^. If r→×a→=b→×r→,r→·αi^+2j^+k^=3 and r→·(2i^+5j^-αk^)=-1,α∈R, then the value of α+|r→|2 is equal to :

Question

Let

\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}

and

\vec{b} = 2 \hat{i} - 3 \hat{j} + 5 \hat{k}

. If

\vec{r} \times \vec{a} = \vec{b} \times \vec{r}, \vec{r} \cdot (α \hat{i} + 2 \hat{j} + \hat{k}) = 3

and

\vec{r} \cdot (2 \hat{i} + 5 \hat{j} - α \hat{k}) = - 1, α \in R,

then the value of

α + | \vec{r} |^{2}

is equal to :

9

15

13

11

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