Question

12. (i) If lines <1,<2 and <3 are such that <1||<3 and <2||<3 then prove that <1||<2. ​

Answer 1

Answer:

3k

x−1

=

1

y−1

=

−5

z−6

are perpendicular, find the value of k

Medium

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Video Explanation

Solution To Question ID 422576

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Answer

The direction of ratios of the lines

−3

x−1

=

2k

y−2

=

2

z−3

and

3k

x−1

=

1

y−1

=

−5

z−6

are −3,2k,2 and 3k,1,−5 respectively.

It is known that two lines with direction ratios a

1

,b

1

,c

1

and a

2

,b

2

,c

2

are perpendicular, if a

1

a

2

+b

1

b

2

+c

1

c

2

=0

∴ −3(3k)+2k×1+2(−5)=0

⇒ −9k+2k−10=0

⇒ 7k=−10

⇒ k=

7

−10

Therefore for k=−

7

10

, the given lines are perpendicular to each other.

Answer 2

Step-by-step explanation:

See this attachment..

Hope its help..