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Chapter 10: Q. 11 (page 823)

If $||u \times v|| = ||u|| ||v||$ , what is the geometric relationship between u and v?

Short Answer

Expert verified

The vectors u and v are orthogonal.

Step by step solution

01

Step 1. Given Information

If $||u \times v|| = ||u|| ||v||$ , what is the geometric relationship between u and v?

02

Step 2. As we know u×v=uvsinθ

If $||u \times v|| = ||u|| ||v||$ then

$\sin θ = 1 θ = 90^{o}$

Then the relation between u and v, $u \times v$ is perpendicular to any plane containing both u and v.

The vectors u and v are orthogonal.

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Most popular questions from this chapter

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.

Find a vector of length 3 that points in the direction opposite to $<1, - 2, 3>$ .

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

Find $\vec{P Q}$

$P = (1, - 2, 5), Q = (1, - 7, - 2)$

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.

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

See all solutions

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