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Chapter 10: Q 10 (page 848)

For vectors u and v in $ℝ^{3}, u . (u \times v) =and v . (u \times v) =$

Short Answer

Expert verified

The required expressions are:

$u . (u \times v) = 0 and v . (u \times v) = 0$

Step by step solution

01

Given information

Two vectors v and u in $ℝ^{3}$ .

02

Filling in the blanks

As cross product of two vectors is orthogonal to both the vectors:

$u . (u \times v) = 0 and v . (u \times v) = 0$

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Most popular questions from this chapter

Find the norm of the vector. $v = (0, 0, 6)$

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

$u = <1, 2>, v = <3, 5>$

Find a vector in the direction opposite to $<- 4, 5, - 1>$ and with magnitude 3.

Use the Intermediate Value Theorem to prove that every cubic function $f (x) = A x^{3} + B x^{2} + C x + D$ has at least one real root. You will have to first argue that you can find real numbers a and b so that f(a) is negative and f(b) is positive.

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?

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