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Find $ \mid u \times v \mid $ and determine whether $ u \times v $ is directed into the page or out of the page.

$ \mid v \mid = 5 $$ \mid u \mid = 4 $

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$|\mathbf{u} \times \mathbf{v}|=10 \sqrt{2}$The vector $\mathbf{u} \times \mathbf{v}$ must point out of the page.

01:34

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Vectors

Johns Hopkins University

Campbell University

University of Michigan - Ann Arbor

Boston College

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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Hello. Welcome to this lesson in this lesson finding the cross ball that the magnitude of the cost at the cross border at you was vain. So this has given us the magnitude of you times the magnitude of a sigh. Feta. Okay, so you called me magnitude is giving us the The magnitude of you is mhm. Mhm. Yeah. Oh, is four The magnitude of way is given us five. Then we have signed 45. So let's look at signed 45 in terms of radicals. Oh, yeah. Okay. Oh, so we have four times five is 20 then signed 45? Yes. Opposite source of sheet over. Hypertension of soul of seats one the opposite of the angle I put on us. Screw it off to So the whole thing is 20 over square root of 2/2. I was scared of tube. So this can be given us. You multiply there. It's covered by the skirt of two by the denominator in the numerator so that we can rationalize the whole thing. So we have scare. We talked. Yeah. You have 20 scourged of to Oliver too? Yeah, so here. That stands courage off. Two cool where I saw this. Is there the magnitude of the cost for that, then the cross for that You, cause me is out of this directed out of the pitch. Okay, so thanks for your time. This is the end of the lesson.

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