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Problem 10 Easy Difficulty

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

$ k \times (i - 2j) $

Answer

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

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Video Transcript

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.