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Chapter 10: Q 4 (page 848)

Find the distance between the points (4, 6, 2) and (1, 3,-5).

Short Answer

Expert verified

The required distance is $\sqrt{67}$ .

Step by step solution

Given information

Given two points in $ℝ^{3}, (4, 6, 2) a n d (1, 3, - 5)$

Finding the distance

As per formula, the required distance is:

$\sqrt{{(1 - 4)}^{2} + {(3 - 6)}^{2} + {(- 5 - 2)}^{2}}$

Simplify:

$\sqrt{67}$

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Most popular questions from this chapter

If u and v are nonzero vectors in $ℝ^{3}$ , why do the equations role="math" localid="1649263352081" $u \cdot (u \times v) = 0$ and $v \cdot (u \times v) = 0$ tell us that the cross product is orthogonal to both u and v?

Find the norm of the vector. $v = (3, - 4)$

What is meant by the triangle determined by vectors u and v in $ℝ^{3}$ ? How do you find the area of this triangle?

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The sum formulas in Theorem 4.4 can be applied only to sums whose starting index value is $k = 1$ .

(b) True or False: $\sum_{k = 0}^{n} \frac{1}{k + 1} + \sum_{k = 1}^{n} k^{2}$ is equal to $\sum_{k = 0}^{n} \frac{k^{3} + k^{2} + 1}{k + 1}$ .

(c) True or False: $\sum_{k = 1}^{n} \frac{1}{k + 1} + \sum_{k = 0}^{n} k^{2}$ is equal to $\sum_{k = 1}^{n} \frac{k^{3} + k^{2} + 1}{k + 1}$ .

(d) True or False: $(\sum_{k = 1}^{n} \frac{1}{k + 1}) (\sum_{k = 1}^{n} k^{2})$ is equal to $\sum_{k = 1}^{n} \frac{k^{2}}{k + 1}$ .

(e) True or False: $\sum_{k = 0}^{m} \sqrt{k} + \sum_{k = m}^{n} \sqrt{k}$ is equal to $\sum_{k = 0}^{n} \sqrt{k}$ .

(f) True or False: $\sum_{k = 0}^{n} a_{k} = - a_{0} - a_{n} + \sum_{k = 1}^{n - 1} a_{k}$ .

(g) True or False: ${(\sum_{k = 1}^{10} a_{k})}^{2} = \sum_{k = 1}^{10} a_{k}^{2}$ .

(h) True or False: $\sum_{k = 1}^{n} {(e^{x})}^{2} = \frac{e^{x} (e^{x} + 1) (2 e^{x} + 1)}{6}$ .

How is the determinant of a 3 × 3 matrix used in the computation of the determinant of two vectors $u = (u_{1}, u_{2}, u_{3}) and v = (v_{1}, v_{2}, v_{3})$ ?

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Find the distance between the points (4, 6, 2) and (1, 3,-5).

Short Answer

Step by step solution

Given information

Finding the distance

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