Chapter 3: Q3P (page 112)

In Problems 1 to 5, all lines are in the $(x, y)$ plane.
3. Write, in parametric form [as in Problem 1], the equation of the straight line that joins $(1, - 2)$ and $(3, 0) .$

Short Answer

Expert verified

The parametric equation of line is $(3 i) + (i + j) t$ .

Step by step solution

Concept of the straight line in slope form.

Write the expression of slope.

$\frac{y - y_{o}}{x - x_{o}} = m$ ………… (1)

Here, $m$ is the slope and $x_{0}$ and $y_{0}$ are the coordinates.

Substitute the values in slop equation 1 and 2

First point is $(1, - 2)$ and the second point is $(3, 0)$ .

Substitute -2 for $y_{0}$ ,1 for $x_{0}$ ,0 for $y_{1} \sqrt{2}$ and 3 for $x_{1}$ , in equation (1).

\frac{0 - (- 2)}{3 - 1} = m m = 1

Substitute 0 for $y_{o},$ 3 for $x_{o},$ and 1 for $m$ in equation (1).

$\frac{y - 0}{x - 3} = 1 \frac{y}{1} = \frac{x - 3}{1}$

Thus, $a = 1$ and $b = 1$ in parametric form.

Substitute the values in parametric form

The parametric form is, $x = 3 + t$ .

And, $y = t$ .

Thus, the parametric equation can be written as follows:

$r = (3, 0) + (1, 1) t$

Therefore, the parametric equation of the line is $(3 i) + (i + j) t$ .

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In Problems 1 to 5, all lines are in the $(x, y)$ plane.
3. Write, in parametric form [as in Problem 1], the equation of the straight line that joins $(1, - 2)$ and $(3, 0) .$

Short Answer

Step by step solution

Concept of the straight line in slope form.

Substitute the values in slop equation 1 and 2

Substitute the values in parametric form

One App. One Place for Learning.

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In Problems 1 to 5, all lines are in the (x,y) plane.3. Write, in parametric form [as in Problem 1], the equation of the straight line that joins (1,-2)and (3,0).

Short Answer

Step by step solution

Concept of the straight line in slope form.

Substitute the values in slop equation 1 and 2

Substitute the values in parametric form

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Measurements

Physics of Motion

Classical Mechanics

Further Mechanics and Thermal Physics

Radiation

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

In Problems 1 to 5, all lines are in the $(x, y)$ plane.
3. Write, in parametric form [as in Problem 1], the equation of the straight line that joins $(1, - 2)$ and $(3, 0) .$