Chapter 3: Q4P (page 112)

In Problems 1 to 5, all lines are in the $(x, y)$ plane.
4. Write, in parametric form, the equation of the straight line that is perpendicular to $r = (2 i + 4 j) + (i - 2 j) t$ and goes through $(1, 0) .$

Short Answer

Expert verified

The parametric form of the equation is $r = i + (2 i + j) t$ .

Step by step solution

Concept of slop of the line

Slope of the line of the form $a i + b j$ is $m = \frac{b}{a}$ .

Product of slopes of two perpendicular lines is $m_{1} m_{2} = - 1$ .

Determine the parametric form

The equation of line is $r = (2 i + 4 j) + (i - 2 j) t$ and passing through $(1, 0)$ .

Let $L = (i - 2 j)$ .

The slope of line $L$ is $m = \frac{- 2}{1} = - 2$ .

Then the slope of line perpendicular to $L$ is $\frac{- 1}{m} = \frac{1}{2}$ .

Then the equation of line perpendicular to $L$ is $L_{1} = (2 i + j)$ .

The line passing through $(1, 0)$ and parallel to $L_{1} = (2 i + j)$ is,

$\frac{1}{2} = \frac{y - 0}{x - 1}$ $(∵ \frac{y - y_{1}}{x - x_{1}} = m)$

$\frac{x - 1}{2} = y$

Hence, the parametric form of the equation is $r = i + (2 i + j) t$ .

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In Problems 1 to 5, all lines are in the $(x, y)$ plane.
4. Write, in parametric form, the equation of the straight line that is perpendicular to $r = (2 i + 4 j) + (i - 2 j) t$ and goes through $(1, 0) .$

Short Answer

Step by step solution

Concept of slop of the line

Determine the parametric form

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Most popular questions from this chapter

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In Problems 1 to 5, all lines are in the (x,y) plane.4. Write, in parametric form, the equation of the straight line that is perpendicular to r=(2i+4j)+(i-2j)tand goes through (1,0).

Short Answer

Step by step solution

Concept of slop of the line

Determine the parametric form

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Work Energy and Power

Oscillations

Turning Points in Physics

Physics of Motion

Translational Dynamics

Solid State Physics

Study anywhere. Anytime. Across all devices.

In Problems 1 to 5, all lines are in the $(x, y)$ plane.
4. Write, in parametric form, the equation of the straight line that is perpendicular to $r = (2 i + 4 j) + (i - 2 j) t$ and goes through $(1, 0) .$