Question

P
=
948.46)
Yz-
plane
clivides
AB is the
ratio
2:3
in
the Yz
2 Find the patio
which
line
plane
cuivides
the
segment
the
formed by
points
(-29497) and (39-598)
joining the​

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

1y1,z1) and B(x2,y2,z2) in the ratio m:n is=( m+nmx2+nx1

m+my2+nym+nmz2+nz)

Here,m:n=k:1A(x1,y1,z1)=(1,2,3)

B(x2,y2,z2)=(−3,4,−5)

Then the co-ordinate ofP(x,y,z)=(k+1k×(−3)+1(1),

k+1k×(4)+1×(2),k+1k×(−5)+1×(3)

k+1−3k+1,k+14k+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+14k+2,

k+1−5k+3

Then, Comparing and we get,

k+1−3k+1=0

−3k+1=0

−3k=−1

k= 31

Then, k:1=1:3

Hence, this is the answer