Question

find the point of intersection of the line r = 2a + b + t( b- c) and plaine r = a+x(b+c) +y (a + 2b- 2c ) where abc arr

Answer 1

Answer:

r

=

a

+λ(

b

−

a

) (equation of a line)

So, the 2 intersecting lines are,

r

1

=(2a+3b−c)+λ((3a+4b−2c)−(2a+3b−c))=(2a+3b−c)+λ(a+b−c)

and

r

2

=(a−2b+3c)+μ((a−6b+6c)−(a−2b+3c))=(a−2b+3c)+μ(−4b+3c)

At the point of intersection,

r

1

=

r

2

.

ie, (2a+3b−c)+λ(a+b−c)=(a−2b+3c)+μ(−4b+3c)