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Chapter 10: Q 9 (page 848)

Fill in the blanks:
For any vectors u and vin $ℝ^{3}$ and any scalar c, $c (u \times v) ==$

Short Answer

Expert verified

The required expression is $c (u \times v) = (c u) \times v = u \times (c v)$

Step by step solution

01

Given information

Given two vectors u and v in $ℝ^{3}$ and a scalarc.

02

Filling in the blanks

As per the multiplication of a scalar with a cross product:

$c (u \times v) = (c u) \times v = u \times (c v)$

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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.

(c) The area of the triangle determined by the points.

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

In Exercises 24-27, find ${comp}_{u} v, {proj}_{u} v$ and the component of v orthogonal tou.

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

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

localid="1649405204459" role="math" $(u \times v) \cdot w and u \cdot (v \times w)$

Use the definition of the derivative to find $f'$ for each function $f$ in Exercises 39-54

$f (x) = \frac{2}{x + 1}$

Calculate the limits in Exercises $25 - 28$ , using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.

localid="1648227587052" $\lim_{x \to 0} \frac{3}{2 x^{2} - 4 x + 1}$ .

See all solutions

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