   Chapter 12.1, Problem 78E

Chapter
Section
Textbook Problem

# Writing a Transformation In Exercises 75–78, consider the vector-valued function r ( t ) = t 2 i + ( t − 3 ) j + t k . Write a vector-valued function s(t) that is the specified transformation of r.A horizontal translation five units in the direction of the positive y-axis

To determine

To calculate: The vector valued function, s(t) that is a horizontal transformation of r(t)=t2i+(t3)j+tk, five unit in the direction of positive x-axis.

Explanation

Given:

The vector valued function is: r(t)=t2i+(t3)j+tk. The horizontal transformation two units in the direction of negative x-axis.

Calculation:

Consider the provider vector value function,

r(t)=t2i+(t3)j+tk.

Compare the above equation with the standard equation r(t)=f(t)i+g(t)j+tk. Here, f(t)=t2,g(t)=(t3) and h(t)=t.

When horizontal transformation k unit in the direction of positive x-axis then, the vector moves k units along the x-axis in the positive direction.

f(t)+k=t2+k

Where, k0

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