   Chapter 16.6, Problem 19E

Chapter
Section
Textbook Problem

Find a parametric representation for the surface.19. The plane through the origin that contains the vectors i − j and j − k

To determine

To find: The parametric representation for the surface of the plane that passes through the origin and contains the vectors ij and jk .

Explanation

Given data:

The surface of the plane that passes through the origin and contains the vectors ij and jk .

Formula used:

Write the expression to find parametric representation for the surface of the plane that passes through the point (x0,y0,z0) and contains the vectors a=a1,a2,a3 and b=b1,b2,b3 .

x=x0+ua1+vb1,y=y0+ua2+vb2,z=z0+ua3+vb3 (1)

Here,

u and v are scalar parameters.

From the given data, the point (x0,y0,z0) is (0,0,0) .

Consider the vector ij as a and write the vector follows.

a=i+(1)j+(0)k=1,1,0

Consider the vector jk as b and write the vector follows

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