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Question

If $$A = (1, 2, 3), B = (2, 10, 1)$$, $$Q$$ are collinear points and $$Q_x=-1$$, then $$Q_z=$$


A
3
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B
7
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C
14
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D
7
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Solution

The correct option is A $$7$$
The direction ratios of the line $$AB$$ are $$ (2-1) : (10-2) : (1-3) = 1 : 8 : -2 $$.

Hence, any point $$Q$$ lying on the line $$AB$$ can be written in the form of $$(1+k, 2+8k, 3-2k)$$, where $$k$$ is a real number.

$$Q_x = -1 $$

Hence, $$1+k = -1$$ 

This gives, $$k = -2$$.

$$ {Q}^{}_{z}  = 3- (2\times (-2)) = 7$$

Hence, option B is correct.

Mathematics

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