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Question

The angle between the lines x+21=y+32=z41 and x+11=y1=z0 is

A
π6
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B
π3
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C
π2
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D
0
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Solution

The correct option is D π6
Angle between the lines l1=xx1a1=yy1b1=zz1c1 and l2=xx2a2=yy2b2=zz2c2 is given by
cosθ=|a1a2+b1b2+c1c2|a21+b21+c21a22+b22+c22
Angle between the lines x+21=y+32=z41 and x+11=y1=z0 is
cosθ=|1(1)+(2)1+1(0)|(1)2+(2)2+(1)2(1)2+(1)2+(0)2
cosθ=|12|62
cosθ=|33|62
cosθ=32
θ=cos1(32)=cos1(32)=π6
θ=π6.

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