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Find vectors V,w such that V+w=(-3,2) and vespan(2,-1) and 1(2,-1)e)Suppose thatIlv/l-2, Ilwll-1,and vLw . Find (-v+Sw) (3v-7w)-...

Question

Find vectors V,w such that V+w=(-3,2) and vespan(2,-1) and 1(2,-1)e)Suppose thatIlv/l-2, Ilwll-1,and vLw . Find (-v+Sw) (3v-7w)-

Find vectors V,w such that V+w=(-3,2) and vespan(2,-1) and 1(2,-1) e) Suppose thatIlv/l-2, Ilwll-1,and vLw . Find (-v+Sw) (3v-7w)-



Answers

Compute the dot product of the vectors $\mathbf{u}$ and $\mathbf{v},$ and find the angle between the vectors. $$\mathbf{u}=\langle-10,0,4\rangle \text { and } \mathbf{v}=\langle 1,2,3\rangle$$

Okay. This question wants us to find the dot product between these two vectors and then the angle between them. So for the dot product, we just take some of, ah, like components multiplied together. So first to multiply the axe components, then we add that to the white components being multiplied. Then we add that to the product of Z components. So our dot product is just negative 10 plus seven plus 12 rather which is to so then we can find the angle through the formula you dot the is equal to the magnitude of you times the magnitude of v. Times Co sign data. So we need to find each of our vector magnitudes. So for you, we just take the square root of the sums of the components squares. So you get 10 squared plus zero squared plus four squared again. This is just with a grin there, um, giving us the square root of 116. Then for the magnitude of the similarly we just sum up the square components than square that and this is nine plus 15 or sorry, nine plus five, rather which is 14 under the square root. So now we can plug in for everything because we know that the dot product is too. The magnitude of you is square root. 1 16 The magnitude of V is 14 then we have the coastline data. So that means co sign data is just equal to two over the square root of 1 16 times 14. Giving us data is equal to the inverse co sign of that expression, or an approximate angle of 87.2 degrees.

In this question that Caribbean better WR given and we have to find video. W v B Director V is equal to five I minus four j and the hunter W is equal to minus toe. I minus j. Now we door w is equal toe five multiplied by minus two plus minus four multiplied by minus one, which is equal to minus six. Now we don't V is equal to four. I have multiplied by five last minus for murdered like by minus four, which is equal to 41. Thus, we don't w is equal to minus six, and we'd or V is equal to 41.

In this question the vector V and W are given and we have to find we don't w and we don't be the vector V is equal to three. I bless G and Dr W. I bless three Jim No, we got a blues in Quito three my delight by one bless one multiplied by three It gives us six That's the value off you, daughter Blue six. Now we find you don't me does read or he will be called three multiplied by three bless one multiplied by one which is equal to 10 Does the value of the dollar fee is 10 Does Our final answer is we daughter blue is equal to six and you don't mean is equal to men.

All right. We want to find the vectors U. And V. In component form where the initial and terminal points at each given and then show that they are equivalent. You has initial point negative four negative one. Internal 10.11 84 B has initial 10 13. Terminal 25 1, 10 or 10. This question is challenging understanding of vector geometry or vectors in the plane to solve. We need to understand that for a vector with initial point P I equals X I Y. Ii. And terminal point P T equals X T, Y. T. The component form of the vector is V equals X T minus X I, Y t minus Y. So since we have the coordinates X I X T, Y T Y I. For all of our two vectors, we can go ahead and plug in this equation to solve thus you 11 plus four negative four plus one or 15 negative three. Similarly, V. S 10 minus 13 for 25 minutes, 10. Which comes out to 15 negative three. So since our vectors are 15 negative three and 15 negative three a k a negative components for X, red and white. Green directors, U and V are equivalent.


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