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Find the vector, not with determinants, but by using properties of cross products.

$ k \times (i - 2j) $

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$\mathbf{k} \times(\mathbf{i}-2 \mathbf{j})=2 \mathbf{i}+\mathbf{j}$

01:09

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Vectors

Johns Hopkins University

Baylor University

University of Nottingham

Idaho State University

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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Find the vector, not with …

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Find the vector; not with …

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00:17

Welcome back to another cross product problem where we're going to be calculating the cross product of K and the vector I minus two J. Without doing any of the math. Just using properties. So our first property of cross products is that any time we have K across something else, we can write this as K. Cross I minus K. Cross to J. We can expand the parentheses exactly as you would expect. Now. In order to find K cross I it helps to know that K Is the Vector zero, 01. Look something like this and I as the vector 100 looking something like this. And the right hand rule says, as we curve our fingers of the right hand from K towards I. Then the cross product will be pointing in the direction of our thumb. This will be K cross I and look at that. That's actually just jay. Next we're gonna do a little more algebra. K. Cross to J Is the same thing as two times K cross J. So let's do that. Math again. Kay, is this vector here and J is this factor here. So the right hand rule says, as we curve our fingers from K towards J, that's the fingers of the right hand than the answer is going to be pointing in the direction of our thumb. This is K cross J. And this ends up being the same thing as negative. Hi. And so if we simplify this, our new vector is to I plus jay without any math. Thanks for watching.

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