   Chapter 12.5, Problem 3E

Chapter
Section
Textbook Problem

# Find a vector equation and parametric equations for the line.3. The line through the point (2, 2.4, 3.5) and parallel to the vector 3i + 2j −k

To determine

To find: A vector equation for a line through the point (2,2.4,3.5) and parallel to the vector 3i+2jk and the parametric equations for a line through the point (2,2.4,3.5) and parallel to the vector 3i+2jk .

Explanation

Formula:

Write the expression to find vector equation (r) .

r=r0+tv (1)

Here,

r0 is the position vector of point P0(2,2.4,3.5) and

v is the parallel vector to the line.

Write the expressions to find the parametric equations for a line through the point (x0,y0,z0) and parallel to the direction vector ai+bjck .

x=x0+at,y=y0+bt,z=z0+ct (2)

Write the position vector (r0) using the point P0(2,2.4,3.5) as follows.

r0=2i+2.4j+3.5k

Calculation of vector equation (r) :

In equation (1), substitute 2i+2.4j+3.5k for r0 and 3i+2jk for v .

r=(2i+2.4j+3.5k)+t(3i+2jk)=(2+3t)i+(2

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