Arun Kumar
Last Activity: 10 Years ago
Equation of plane with three points
| x-x1 | | y-y1 | | z-z1 | = 0 |
| x2-x1 | | y2-y1 | | z2-z1 |
| x3-x1 | | y3-y1 | | z3-z1 |
| x- 4 | | y- (-1) | | z -5 | = 0 |
| (-1) - 4 | | 2 - (-1) | | 0 - 5 |
| 1 - 4 | | 1 - (-1) | | 4 - 5 |
| x -4 | | y -(-1) | | z -5 | = 0 |
| -5 | | 3 | | -5 |
| -3 | | 2 | | -1 |
| (x - | 4 | )( | 3 | · | (-1) | - | (-5) | · | 2 | ) - (y - | (-1) | )( | (-5) | · | (-1) | - | (-5) | · | (-3) | ) + (z - | 5 | )( | (-5) | · | 2 | - | 3 | · | (-3) | ) = 0 |
| 7 | (x- | 4 | )+ | 10 | (y- | (-1) | )+ | (-1) | (z- | 5 | ) = 0 |
a
-
b
={
ax
-
bx
;
ay
-
by
;
az
-
bz
}={(-1)-1;2-1;0-4}={-2;1;-4}
Lets a x,y,z lies on the line perpendicular to AB and in the plane
then
x-4,y+1,z-5 will also lie in the plane and perpendicular to AB where x,y,z is location of bird at any time.
dot product of these two point should be zero
=>8x+4y-3z=0
since at some time it becomes collinear with AB
=> triangle formed be A,B and that point will be zero
=>
2x-y+4z=29
also it satisfies the plane so
7x+10y-z=13
solvin all three eq.
x=15/7,y=3/7,z=44/7
distance =
divide by velocity to get the answer
Arun KumarIIT Delhi
Askiitians Faculty
