Question

Consider the line given by the parametric equation x = 5 - 2t, y = 3 + t, z = 4t and the plane ax + by + cz = d. Find values for a, b, c and d such that: (a) The plane is perpendicular to the line. (b) The plane is perpendicular to the line and passes through the point (5, 3, 0). (c) The plane is parallel to the line.

          Consider the line given by the parametric equation
x = 5 - 2t, y = 3 + t, z = 4t
and the plane ax + by + cz = d. Find values for a, b, c and d such that:
(a) The plane is perpendicular to the line.
(b) The plane is perpendicular to the line and passes through the point (5, 3, 0).
(c) The plane is parallel to the line.

Consider the line given by the parametric equation
x = 5 - 2t, y = 3 + t, z = 4t
and the plane ax + by + cz = d. Find values for a, b, c and d such that:
(a) The plane is perpendicular to the line.
(b) The plane is perpendicular to the line and passes through the point (5, 3, 0).
(c) The plane is parallel to the line.

Added by Claudia O.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/26/2023

Step 1

We can do this by taking the derivative of the parametric equations with respect to t: $\frac{dx}{dt} = 2, \frac{dy}{dt} = 1, \frac{dz}{dt} = 4$ So the direction vector of the line is $\mathbf{v} = \langle 2, 1, 4 \rangle$. Now, we want to find a plane that is Show more…

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Consider the line given by the parametric equation x = 5 - 2t, y = 3 + t, z = 4t and the plane ax + by + cz = d. Find values for a, b, c and d such that: (a) The plane is perpendicular to the line. (b) The plane is perpendicular to the line and passes through the point (5, 3, 0). (c) The plane is parallel to the line.