Question

16. Show that the following two lines intersect
X~9
z-18 x-5 11
13)
y-
7+6
몇
-​

Answer 1

Answer:

ANSWER

Let's first represent equations of lines in the vector form,

First line →

r

=(

i

^

−

j

^

)+λ(2

i

^

+3

j

^

+

k

^

)

Second Line →

r

=(−

i

^

+2

j

^

+2

k

^

)+μ(5

i

^

+

j

^

)

Let's now assume that that lines intersect for λ=λ

1

and μ=μ

1

Then, (2λ

1

+1)

i

^

+(3λ

1

−1)

j

^

+λ

1

k

^

=(5μ

1

−1)

i

^

+(5μ

1

+2)

j

^

+2

k

^

Equating we get,

2λ

1

+1=5μ

1

−1 ......(1)

3λ

1

−1=5μ

1

+2 ....(2)

λ

1

=2...... (3)

Solving equation (2) and (3), We get λ

1

=2 and μ

1

=

5

3

which doesn't satisfy the equation (1) which is a contradiction .

Thus the above lines are skew lines i.e they neither intersect nor are parallel to each other .

Step-by-step explanation:

hope this will help you

Answer 2

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