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Applications of Cross Product

If A1,2,3, B2...

Question

If $A (1, 2, 3), B (2, 10, 1), Q$ are collinear points and $Q_{x} = - 1$ then $Q_{z} =$

- 3

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7

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14

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Solution

The correct option is B $7$
For collinear points:
$\frac{x_{3} - x_{1}}{x_{2} - x_{1}} = \frac{y_{3} - y_{1}}{y_{2} - y_{1}} = \frac{z_{3} - z_{1}}{z_{2} - z_{1}}$
$\Rightarrow \frac{- 1 - 1}{2 - 1} = \frac{Q_{z} - 3}{1 - 3}$
$\Rightarrow \frac{- 2}{1} = \frac{Q_{z} - 3}{- 2}$
$\Rightarrow Q_{z} = 4 + 3 = 7$

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A = (1, 2, 3), B = (2, 10, 1)

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