1. The problem statement, all variables and given/known data
Find an equation of the plane that passes through the points (4,2,1) and (-2, 9, 6), and is parallel to the z axis.
2. Relevant equations
a(X-Xo) + b(Y-Yo) + c(Z-Zo) = 0
3. The attempt at a solution
Okay so for this one, I first tried to make a vector out of the two given points.
If P(4,2,1) and Q(-2,9,6),
then PQ = <-6,7,5>.
Next I fumbled around a bit trying to figure out how to either a) find another vector to form a cross product with, or b) somehow figure out what the <a,b,c> numbers should look like in order to be parallel to z axis.
When I tried approach a) I came up with another point on the z axis, (0,0,1), used it as a vector of its own, crossed it with PQ, picked up the resultant, and plugged in the direction numbers to the plane equation.
For part b) I tried making a vector out of (0,0,1) and P, crossing it with PQ and using the resultant direction numbers.
However, both approaches seem to be rather wrong.
Find an equation of the plane that passes through the points (4,2,1) and (-2, 9, 6), and is parallel to the z axis.
2. Relevant equations
a(X-Xo) + b(Y-Yo) + c(Z-Zo) = 0
3. The attempt at a solution
Okay so for this one, I first tried to make a vector out of the two given points.
If P(4,2,1) and Q(-2,9,6),
then PQ = <-6,7,5>.
Next I fumbled around a bit trying to figure out how to either a) find another vector to form a cross product with, or b) somehow figure out what the <a,b,c> numbers should look like in order to be parallel to z axis.
When I tried approach a) I came up with another point on the z axis, (0,0,1), used it as a vector of its own, crossed it with PQ, picked up the resultant, and plugged in the direction numbers to the plane equation.
For part b) I tried making a vector out of (0,0,1) and P, crossing it with PQ and using the resultant direction numbers.
However, both approaches seem to be rather wrong.
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