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Chapter 10: Q 6 TB (page 800)

Find the distance between the points (5,-2,-1) and (3, 0,-4).

Short Answer

Expert verified

The required distance is $\sqrt{17} .$

Step by step solution

Given information

The given points are (5,-2,-1) and (3, 0,-4).

Finding the distance

The distance between the given points is:

$\sqrt{{(3 - 5)}^{2} + {(0 - (- 2))}^{2} + {(- 4 - (- 1))}^{2}}$

Simplifying:

$\sqrt{4 + 4 + 9}$

Simplifying further:

$\sqrt{17}$

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Most popular questions from this chapter

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

role="math" localid="1649400253452" $(u \times v) \times w and u \times (v \times w)$

Find a vector in the direction of $<9, 0, - 6>$ and with magnitude 7.

Fill in the blanks to complete each of the following theorem statements:

For $ε > 0, f (x) \in (L - ε, L + ε)$ if and only if $< ε .$

Consider the sequence of sums $\frac{1}{3}, \frac{1}{3} + \frac{1}{9}, \frac{1}{3} + \frac{1}{9} + \frac{1}{27}, \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81}, \dots$

(a) What happens to the terms of this sequence of sums as k gets larger and larger?

(b) Find a sufficiently large value of k which will guarantee that every term past the kth term of this sequence of sums is in the interval (0.49999, 0.5).

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

$u = <2, 0, - 5>, v = <- 3, 7, - 1>$

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Find the distance between the points (5,-2,-1) and (3, 0,-4).

Short Answer

Step by step solution

Given information

Finding the distance

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Most popular questions from this chapter

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