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Chapter 12: Problem 28

Find an equation of the line segment joining the first point to the second point. $$(-1,-8,4) \text { and }(-9,5,-3)$$

Short Answer

Expert verified
Answer: The parametric equations of the line segment joining these two points are: $$x = -1 - 8t$$ $$y = -8 + 13t$$ $$z = 4 - 7t$$

Step by step solution

01

Find the direction vector

To find the direction vector, subtract the position vectors of the two given points: \(\vec{d} = (-9 -(-1), 5 -(-8), -3 - 4) = (-8, 13, -7)\) Now we have the direction vector \(\vec{d} = (-8, 13, -7)\).
02

Write the parametric form of the equation of the line

The parametric equation of the line can be written using one of the given points and the direction vector. We will use point \((-1,-8,4)\) and the direction vector \(\vec{d} = (-8, 13, -7)\). Parametric equations of the line are: $$x = -1 - 8t$$ $$y = -8 + 13t$$ $$z = 4 -7t$$ Now we have the equations of the line segment joining the given points: $$x = -1 - 8t$$ $$y = -8 + 13t$$ $$z = 4 -7t$$

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Most popular questions from this chapter

Prove the following identities. Assume that \(\mathbf{u}, \mathbf{v}, \mathbf{w}\) and \(\mathbf{x}\) are nonzero vectors in \(\mathbb{R}^{3}\). $$(\mathbf{u} \times \mathbf{v}) \cdot(\mathbf{w} \times \mathbf{x})=(\mathbf{u} \cdot \mathbf{w})(\mathbf{v} \cdot \mathbf{x})-(\mathbf{u} \cdot \mathbf{x})(\mathbf{v} \cdot \mathbf{w})$$

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