Question

Find the angle between the lines x/1=y/2 =z/3 and (x+1)/2=(y-3)/-7=(z+2)/7 ​

Answer 1

Answer:

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Answer 2

Given lines are

1

x−7

=

−5

y+3

=

3

z

...(i)

and

−7

2−x

=

2

y

=

1

z+5

⇒

7

x−2

=

2

y

=

1

z+5

...(ii)

DR's of line equations (i) and (ii) are

(a

1

,b

1

,c

1

)=(1,−5,3)

and (a

2

,b

2

,c

2

)=(7,2,1)

Therefore, cosθ=

a

1

2

+b

1

2

+c

1

2

a

2

2

+b

2

2

+c

2

2

a

1

a

2

+b

1

b

2

+c

1

c

2

=

1

2

+(−5)

2

+(3)

2

(7)

2

+(2)

2

+(1)

2

1×7+(−5)×2+3×1

=

1+25+9

49+4+1

7−10+3

=0

⇒θ=

2

π