Question

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

A
3
B
7
C
14
D
7

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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