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Real Valued Functions

If x⃗ satis...

Question

If $\to x$ satisfying the conditions $\to b$ . $\to x$ = $β$ & $\to b$ x $\to x$ = $\to a$ is $\to x = \frac{(β^{2} - 12) \to b}{{∣ ∣ \to b ∣ ∣}^{2}} + \frac{\to a \times \to b}{{∣ ∣ \to b ∣ ∣}^{2}}$ then $β$ can be

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Solution

$\to b . \to x = β$
$\to x = \frac{(β^{2} - 12) \to b}{| \to b |^{2}} + \frac{\to a \times \to b}{| \to b |^{2}}$
$\to b . \to x = β^{2} - 12 = β ⟹ β^{2} - β - 12 = 0 ⟹ β = 4, - 3$

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