Exercise. Find the equation representing the line orthogonal to dı = (2,–1,7) and d2 = (7,1,3) that passes through P= (0,1,2). Express your answer as a vector and as parametric equations. Vector: e(t) = ? +t(-10, Parametric: z(t) = ?, y(t) = ?, z(t) = Exercise. Suppose that we want to give a vector-valued function that traces out the curve described by z= 4y? + 7y - 1. By requiring that y(t) = 4t, find the position vector that traces out this curve. P (t) =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Exercise. Find the equation representing the line orthogonal to dı = (2, –1,7) and d2 = (7,1, 3) that passes through P = (0,1, 2).
Express your answer as a vector and as parametric equations.
Vector: l(t) =
+t(-10,
Parametric: x(t) =
?, y(t) =
?, z(t) =
Exercise. Suppose that we want to give a vector-valued function that traces out the curve described by r = 4y² + 7y – 1.
By requiring that y(t) = 4t, find the position vector that traces out this curve.
P (t) =
Exercise. Find the line that passes through P = (2,-4, 1) parallel to d = (9, 2, 5) using only the given quantities. Express your answer as
a vector and as parametric equations.
Vector: l(t) =
+t
Parametric: z(t) =
?, y(t) =
?, z(t) =
Exercise. Suppose that a bug walks along the parabola y = x? + 3 and does so in a manner in which 4 = 3. If the bug starts walking at
x = 1 at timet = 0, and we want x(t) to measure the bug's x-coordinate at time t, then we have
dt
x(t) =
Transcribed Image Text:Exercise. Find the equation representing the line orthogonal to dı = (2, –1,7) and d2 = (7,1, 3) that passes through P = (0,1, 2). Express your answer as a vector and as parametric equations. Vector: l(t) = +t(-10, Parametric: x(t) = ?, y(t) = ?, z(t) = Exercise. Suppose that we want to give a vector-valued function that traces out the curve described by r = 4y² + 7y – 1. By requiring that y(t) = 4t, find the position vector that traces out this curve. P (t) = Exercise. Find the line that passes through P = (2,-4, 1) parallel to d = (9, 2, 5) using only the given quantities. Express your answer as a vector and as parametric equations. Vector: l(t) = +t Parametric: z(t) = ?, y(t) = ?, z(t) = Exercise. Suppose that a bug walks along the parabola y = x? + 3 and does so in a manner in which 4 = 3. If the bug starts walking at x = 1 at timet = 0, and we want x(t) to measure the bug's x-coordinate at time t, then we have dt x(t) =
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