Question

the point where the line through 341 and 516 crosses the xy plane is​

Answer 1

Answer:

The equation of the line passing through the two points with vector

a

+

b

r

=

a

+λ(

b

−

a

)

since the line passes through the point is:

a

=3

i

^

+4

j

^

+

k

^

and

a

=5

i

^

+

j

^

+6

k

^

(

b

−

a

)=5

i

^

+

j

^

+6

k

^

−

a

=3

i

^

+4

j

^

+

k

^

=2

i

^

−3

j

^

+5

k

^

r

=3

i

^

+4

j

^

+

k

^

+λ(2

i

^

−3

j

^

+5

k

^

).....1

Now,

The coordinates of the point where the line cross the XY plane by (X,Y,0)

so,

r

=x

i

^

+y

j

^

+0

k

^

....2

Since, these are crossing the points so put this value in equation 1 then we get,

x

i

^

+y

j

^

+0

k

^

=3

i

^

+4

j

^

+

k

^

+λ(2

i

^

−3

j

^

+5

k

^

)

Equating the coefficient of the unit vector then,

x=1+5λ...a

y=4−3λ...b

1+5λ=0...c

by solving equation c we get

1+5λ

λ=−

5

1

This is the required solution.