Find the point of intersection of the line r=2a+b+t(b-c) and the plane r=a+x(b=c)=y(a+2b-c)where a,b and c are non coplanar vectors
Answers
Given: the line r = 2a+b+t(b-c) and the plane r = a+x(b+c)+y(a+2b-c)
To find: The point of intersection.
Solution:
- So we have given a line:
r = 2a + b + t ( b - c )
- It can be written as:
r = 2a + ( 1 + t)b + (-t)c .................(i)
- We have also given a plane:
r = a + x ( b + c ) + y ( a + 2b - c )
- It can be written as:
r = (1 + y)a + (x + 2y)b + (x - y)c .................(ii)
- So from (i) and (ii), we have:
1 + y = 2
y = 1
x + 2y = 1 + t
x + 2 = 1 + t
x - t + 1 = 0 .................(iii)
x - y = -t
x - 1 = -t
x + t - 1 = 0 ...................(iv)
- So from (iii) and (iv), we get:
x = 0
- Putting it in iii, we get:
t = 1
- Now from (i), we have:
r = 2a + b + ( b - c ) = 2a + 2b - c
Answer:
So the point of intersection is r = 2a + 2b - c.
Answer:
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Step-by-step explanation:
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