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Chapter 10: Q 8 (page 848)

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

Short Answer

Expert verified

The required expression is $ℝ^{3}, v \times u = - (u \times v)$

Step by step solution

01

Given information

Any two vectors u and v in $ℝ^{3}$ .

02

Filling in the blanks

The cross product of two vectors in $ℝ^{3}$ is anti commutative in nature.

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

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Most popular questions from this chapter

Find $\vec{P Q}$

$P = (- 1, 5, 4), Q = (- 1, 6, 4)$

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.

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

Find the mass of a 30-centimeter rod with square cross sections of side length 2 centimeters, given that the density of the rod x centimeters from the left end is ρ(x) = $10 \cdot 5 + 0 \cdot 01527 x^{2}$ grams per cubic centimeter.

In Exercises 37–42, find $||v||$ and find the unit vector in the direction of v.

$v = <\frac{1}{5}, \frac{1}{3}>$

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