Question

Question 12 (2 marks) Attempt 1 A space curve is defined by C:u)2i+u+3u2k, for u20 Find the Cartesian form of the equation for the plane that is perpendicular to the space curve C at the point where u 1 Your answer should be an equation, expressed in terms of the Cartesian variables x, y and z using the correct syntax. For example: 3*x-2y+5'z-2, or, 2 (x-1)+4 (y-2)+z-1-0, or 3'x+ 6'z-12-y, or y-x+35 (2-256)-20 Do not use decimal approximations all numbers should be entered as exact expressions, for example 5/2 Skipped

Answer 1

For a plane perpendicular to the space curve C, the space curve acts as a normal curve or normal vector at that point.

Let P be any arbitrary point chosen on the plane whose equation is to be found out.

Coordinates of P are given as (x,y,z).

Further,

Consider point A on the plane whose coordinates are given by substituting the value of u equal to 1. This point also lies on the plane.

For the two vectors to be perpendicular their dot product must be zero.

This is how the equation of the plane is calculated in the desired form.

A.づ

For further queries, feel free to comment.

All the best!