Better Students Ask More Questions.
Find an equation for the plane containing the line L:(x-4)/(-4) =(z+3)/2; y = -3 and...
1 Answer | add yours
You need to write the parametric form of the given line, such that:
`l: x = 4 - 4t`
`y = -3 + 0*t`
`z = -3 + 2t`
You need to consider the directional vector of the line using the coefficient of parameter t, such that:
`bar l = <-4,0,2>`
You may find the coordinates of other point P in the plane considering the parameter t = 0, such that:
`P = (4,-3,-3)`
You may evaluate the directional vector `bar (PQ)` such that:
`bar(PQ) = (x_P - x_Q) bar i + (y_P - y_Q) bar j + (z_P - z_Q) bar k`
`bar(PQ) = (4 + 3) bar i + (-3 + 2) bar j + (-3 - 2) bar k`
`bar(PQ) = 7 bar i - bar j - 5 bar k`
You may evaluate the normal vector `bar n` to the plane containing the line and the point Q such that:
`bar n = bar l x bar (PQ)`
`bar n = [(bar i, bar j, bar k),(-4,0,2),(7,-1,-5)]`
`bar n = 4 bar k + 14 bar j + 2 bar i - 20 bar j`
`bar n = 2 bar i - 6 bar j + 4 bar k`
`bar n = <2,-6,4>`
Dividing by 2 yields:
`bar n = <1,-3,2>`
You may write the equation of the plane such that:
`P: (x - x_Q) - 3(y - y_Q) + 2(z - z_Q) = 0`
`P: (x + 3) - 3(y - 2) + 2(z + 2) = 0`
Hence, evaluating the equation of the plane, under the given conditions, yields `P: (x + 3) - 3(y - 2) + 2(z + 2) = 0` .
Posted by sciencesolve on February 2, 2013 at 7:14 AM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.