Question

determine the point at which the line segment joining the point (1, 2,3) and (4, 6-5) is divid by xy - plane​​

Answer 1

Answer:

We have,

Let AB be the line segment joining the points

A(1,2,3) and B(−3,4,−5).

Let XZ−plane divide line AB.at P(x,y,z) in the ratio k:1.

Co- ordinate of point P(x,y,z) that divide line segment joining point A(x

1

,y

1

,z

1

) and B(x

2

,y

2

,z

2

) in the ratio m:n is

=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

,

m+n

mz

2

+nz

1

)

Here,

m:n=k:1

A(x

1

,y

1

,z

1

)=(1,2,3)

B(x

2

,y

2

,z

2

)=(−3,4,−5)

Then the co-ordinate of

P(x,y,z)=(

k+1

k×(−3)+1(1)

,

k+1

k×(4)+1×(2)

,

k+1

k×(−5)+1×(3)

)

=(

k+1

−3k+1

,

k+1

4k+2

,

k+1

−5k+3

)

Since, point P(x,y,z) lie on the XZ−plane

Then, Its Y-coordinate will be zero.

P(0,y,z)=(

k+1

−3k+1

,

k+1

4k+2

,

k+1

−5k+3

)

Then, Comparing and we get,

k+1

−3k+1

=0

−3k+1=0

−3k=−1

k=

3

1

Then, k:1=1:3

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