In vector algebra, what condition must two nonzero vectors satisfy to be mutually perpendicular?

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In algebra, what are the real solutions to the quadratic equation $x^{2} - 7 x + 12 = 0$ ?
In algebra, what is the product of the roots of the quadratic equation $3 x^{2} - 11 x + 6 = 0$ ?
In algebra, what is the sum of the roots of the equation $2 x^{2} - 10 x + 7 = 0$ ?
In algebra, what is the discriminant of the quadratic equation $2 x^{2} - 4 x + 5 = 0$ ?
In algebra, for what value of $k$ does the equation $x^{2} - 6 x + k = 0$ have exactly one real root?
In algebra, what is the solution set of the linear inequality $4 - 2 x \geq 10$ ?