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Chapter 10: Q 31. (page 801)

Find $\vec{P Q}$
$P = (1, - 2, 5), Q = (1, - 7, - 2)$

Short Answer

Expert verified

The required value of $\vec{P Q} = (0, - 5, - 7)$ .

Step by step solution

Step 1. Given information

$P = (1, - 2, 5) a n d Q = (1, - 7, - 2)$ .

Step 2. Find the values of PQ→

$\vec{P Q} = (x_{2} - x_{1}, y_{2} - y_{1}, z_{2} - z_{1}) = (1 - 1, - 7 - (- 2), - 2 - 5) = (0, - 5, - 7)$

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Most popular questions from this chapter

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.

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

(Hint: Think of the $x y$ -plane as part of $ℝ^{3}$ .)

In Exercises 30–35 compute the indicated quantities when

$u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

$u \times v and v \times u$

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?

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

Write a delta–epsilon proof that proves that $f$ is continuous on its domain. In each case, you will need to assume that δ is less than or equal to $1$ .

$f (x) = x^{1 / 2}$

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Find $\vec{P Q}$
$P = (1, - 2, 5), Q = (1, - 7, - 2)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the values of PQ→

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Most popular questions from this chapter

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Find PQ→P=1,-2,5,Q=1,-7,-2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the values of PQ→

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Statistics

Applied Mathematics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Find $\vec{P Q}$
$P = (1, - 2, 5), Q = (1, - 7, - 2)$