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Chapter 10: Q 23 (page 789)

Find the distance between the points (1, 4, 7) and (-2, 3, 5).

Short Answer

Expert verified

The required distance is $\sqrt{14}$

Step by step solution

01

Given information

The given two points are (1, 4, 7) and (-2, 3, 5).

02

Finding the required distance

The distance between two points as per formula is:

$\sqrt{{(- 2 - 1)}^{2} + {(3 - 4)}^{2} + {(5 - 7)}^{2}}$

Simplify:

$\sqrt{{(- 3)}^{2} + {(- 1)}^{2} + {(- 2)}^{2}}$

Further simplify:

$\sqrt{14}$

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Most popular questions from this chapter

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

Find the volume of the parallelepiped determined by vectors u, v and w. Do u, v and w form a right-handed triple?

Why do we use the terminology "separable" to describe a differential equation that can be written in the form

If $||u \times v|| = ||u|| ||v||$ , what is the geometric relationship between u and v?

In Exercises 37–42, find $||v||$ and find the unit vector in the direction of v.

$v = <\sqrt{\frac{1}{3}}, - \sqrt{\frac{2}{3}}>$

If u and v are vectors in $ℝ^{3}$ such that $u \cdot v = 0$ and $u \times v = 0$ , what can we conclude about u and v?

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