Find the real value of $a$ for which vectors $u = 3 i - 2 j$ and $v = 4 i + a j$ are perpendicular.

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In an arithmetic progression $(a_{n})_{n \geq 1}$ , the first term is $a_{1} = 3$ and the common difference is $r = 4$ . What is the tenth term…
In a geometric progression $(b_{n})_{n \geq 1}$ , $b_{1} = 2$ and the common ratio is $q = 3$ . What is the sum of the first 4 terms $S_{4}$ ?
What are the coordinates of the vertex of the parabola associated with $f (x) = x^{2} - 4 x + 3$ ?
If $x_{1}$ and $x_{2}$ are the roots of $x^{2} - 5 x + 6 = 0$ , what is the value of $\frac{1}{x _{1}} + \frac{1}{x _{2}}$ ?
What is the real solution of the logarithmic equation $lo g_{2} (x^{2} - 1) = 3$ ?
What is the solution of the exponential equation $3^{2 x - 1} = 27$ ?

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