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Chapter 10: Q 21 (page 789)

To find the distance between the points (-2, 3) and (5, -6).

Short Answer

Expert verified

The required distance is $\sqrt{130}$ .

Step by step solution

Given information

Given two points (-2, 3) and (5, -6).

Finding the distance

The distance between given two points as per formula:

$\sqrt{(5 - {(- 2))}^{2} + (- {6 - 3)}^{2}}$

Simplify:

$\sqrt{{(7)}^{2} + (- {9)}^{2}}$

Simplify further:

$\sqrt{130}$

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Most popular questions from this chapter

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

role="math" localid="1649434688557" $v \times w and w \times v$

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

$u \times w and w \times u$

In Exercises 36–41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

$P (1, 4, 6), Q (- 3, 5, 0), R (3, 2, - 1)$

Suppose that we know the reciprocal rule for limits: If $\lim_{x \to c} g (x) = M$ exists and is nonzero, then $\lim_{x \to c} \frac{1}{g (x)} = \frac{1}{M}$ This limit rule is tedious to prove and we do not include it here. Use the reciprocal rule and the product rule for limits to prove the quotient rule for limits.

Find a vector of length 3 that points in the direction opposite to $<1, - 2, 3>$ .

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To find the distance between the points (-2, 3) and (5, -6).

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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