Status: Tags: #math232/questions/midterm Links: Math 232 Midterm 1 Study Plan
MATH 232 Midterm 1 Practice 2
Principles
3
3a
Find scalar equation of plane that contains two points (1,2,3) and (1,-1,1) ?
- Create scalar equations from the points given
- Move d to LHS, act as $x_4$
- Augmented matrix and RREF
- Find solution
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3b
Write down the equation of a plane that is parallel to the vector v=(2,1,-3) and contains the point (1,1,1) ?
- Given parallel, we can find normal through n(v) = 0
- Plug into scalar eqn, just need to find d
- Can be done by plugging in point
- Plug into scalar eqn, just need to find d
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3c
Find intersection of two lines x(t) = (1,-2) + t(2,1) r(s) = (2,0) + s(1,1) ?
- Set the two equations equal to eachother
- Convert into parametric equations, move variables to LHS and constants to RHS
- Convert into augmented matrix
- Find free variable values, plug into original parametric to make sure LHS = RHS
- Intersection is found variables
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4a
Given plane 2x - y + 2z = 4 Find a plane (vector equation) that passes through the point (1,-1,2) and is parallel to this plane ?
- Find normal through n(v) = 0
- Plug in point and normal !
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4b
Find intersection of r(t) = (2, -2, 1) + t(-3, 1, 1) and plane 2x - y + 2z = 4 ?
- Find parametric equation of r(t) (x,y,z)
- Plug into plane to find t
- Find value of the point of intersection by plugging t into para eqn (x,y,z)
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Created:: 2022-02-10 15:46