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Question

The shortest distance between the z-axis and the line x+y+2z−3=0,2x+3y+4z−4, is

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is A 2
Any two point on the line x+y+2z3=0,2x+3y+4z4 are (1,2,2) and (5,2,0)

Thus its equation may be written as, x54=y+20=z2

and equation of line z-axis is, x0=y0=z1

Now we know shortest distance between two line is given by, D=(ac).(b×d)|b×d|

Here a=0,d=4i2k,b=k,c=5i2j

b×d=∣ ∣ ∣^i^j^k001402∣ ∣ ∣=4^j

Thus D=(5^i2^j).(4^j)|4^j|=84=2

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