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Perpendicular Distance of a Point from a Line

If 1x-11x-12x...

Question

If $\frac{1}{(x - 11) (x - 12) (x - 13)} = \frac{A}{x - 11} + \frac{B}{x - 12} + \frac{C}{x - 13},$ then the volume of parallelopiped whose adjacent sides are $A^i + B^j + 2 C^k, 2 A^i - B^j,^i - 3 B^j + 4 C^k$ is (in cu. units)

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Solution

We have,
$\frac{1}{(x - 11) (x - 12) (x - 13)} = \frac{A}{x - 11} + \frac{B}{x - 12} + \frac{C}{x - 13}$
$\Rightarrow A = \frac{1}{2}, B = - 1, C = \frac{1}{2}$
$∴$ Volume of parallelopiped
$= ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{1}{2} & - 1 & 1 1 & 1 & 0 1 & 3 & 2 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ = 5 cu. units$

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\frac{1}{(x - 11) (x - 12) (x - 13)} = \frac{A}{x - 11} + \frac{B}{x - 12} + \frac{C}{x - 13}

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Perpendicular Distance of a Point from a Line

Standard XII Mathematics

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