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Find Ilv-wl; ifv = - 2i + 5j and w = 2i 6jIlv wllL...

Question

Find Ilv-wl; ifv = - 2i + 5j and w = 2i 6jIlv wllL

Find Ilv-wl; ifv = - 2i + 5j and w = 2i 6j Ilv wll L



Answers

Find $ a \cdot b $.

$ a = 2i + j $ , $ b = i - j + k $

Okay, were given the use equal to three over four W W is equal to I put two j but if you could do one come to So let's put that in to be over for times one comes to it gives us three over four comma. Three over two. Okay. And I were asked if I'd a component for him, but this is already in component for him. And I always need to. Graff are solution. So we have. We were four. How much is that? But war is about point 75 So that if this is one, this is around 10.75 You're right. And then three over, two up. So this is too. This is one. This is 1.5, which is three too. That would get something like this.

Okay, so this question wants us to take these vectors U. And W. And then find the vector V equals one half times the quantity three U plus W. So let's just start by substituting are factors. And so vector U. As to I hat minus J. Hat plus W. Which is I had Plus two J. Had. And then if we distribute our three inside, we get six I hat -3 J. Hat plus I had Plus two J. Hat. And then collecting like terms inside, we get seven I hat minus J. Hat and then we distribute the one half to get seven halves. I had minus one half jihad. So this is our vector and now it wants us to make a sketch of this, So we need to go 7/2 over. So that's oh Between three and 4 and then 1/2 unit down. So something like that. So that's our vector V.

Okay, This question gives us these two vectors, and it wants us to find the vector V given this linear combination. So first, let's just write out what we're gonna have to do here. So it's 1/2 times, three times you, which is Thio. I had minus J hat plus w wishes I had plus two j hat. So now let's expand everything out inside these brackets, which gives us 1/2 times six. I had minus three j hat Plus I had plus two J hat and this is equal to 1/2 times seven I had minus Jay had which is equal to the factor. Seven halves, negative, 1/2. So now that we have our vector, it wants us to scratch it under a white board here. So we're looking for seven halves, comma, negative, 1/2. So we go over three and 1/2 and down 1/2 so our vector will end up looking something like this. In the survey, actor v.

Okay. This question gives us two factors, you and W. And it gives us some operations to d'oh. So the first operation at once is the vector. V equals 03 halves times you so we can write. This is three halves times the factor. Well, it's in Unit Vector for him. Sold, right? Two. I had minus J hat. And then all we do is distribute the three halves of each term. So we'll get three. I had minus three halves, J head, and then we'll just fix this I because it looks a little messy. So this is our factor VII, and now it wants us to plot it. So v is three. I had minus three has J Head. So it's gonna be something like this. The Tzar vector v.


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