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Question 32098: Hi,
1)
What rule do I use to find points on a plane when starting with an equation R3? Say 3x-3y+z=3 or any other equation for that mater.
2)
How do I find the equation of a particular line in R3 in the form r = a + td.
With a direction vector, and the coordinates of a point on a line.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! 1)
What rule do I use to find points on a plane when starting with an equation R3? Say 3x-3y+z=3 or any other equation for that mater.ANY WAY YOU LIKE ..HERE THERE ARE 3 VARIABLES AND ONE EQUATION.SO GIVE 2 VALUES ARBITRARILY TO ANY 2 VARIABLES,PUT IN THE EQN. AND FIND THE 3RD.VARIABLE..THAT IS ALL..SAY PUT X=0=Y...WE GET 3*0+3*0+Z=3...OR Z=3 SO (0,0,3) IS A POINT IN R3 ON THE PLANE....NOW YOU PUT SAY Y=0=Z...WE GET X=1...SO (1,0,0) IS ANOTHER POINT ..LIKE THIS YOU CAN CONTINUE TO GET ANY POINT YOU LIKE.
2)
How do I find the equation of a particular line in R3 in the form r = a + td.
THE ABOVE EQUATION IS IN FACT THE EQN.FOR A STRAIGHT LINE PASSING THROUGH POINT WITH POSITION VECTOR AS A ......AND PARALLEL TO THE DIRECTION OF VECTOR D...IN THIS EQN...t IS A SCALAR MULTIPLIER.IT GIVES THE POSITION VECTOR R OF ANY POINT ON THAT LINE.
YOU BETTER USE CAPITAL LETTERS FOR VECTORS AND SMALL CASE FOR SCALARS...WRITE THE ABOVE EQN. AS
R=A+tD
OK?OR DO YOU WANT A PROOF OF HOW THIS EQN. IS OBTAINED.
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