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Help with vectors?! (1 Viewer)

lousinoa

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Hello guys,
I'm having trouble with these 2 questions regarding vectors. In the second attachment, I believe a) is -7/9 but I'm not sure about b). Any help and answers would be much appreciated.


capture1.PNG

capture2.PNG
 
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Drongoski

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Hello guys,
I'm having trouble with these 2 questions regarding vectors. In the second attachment, I believe a) is -7/9 but I'm not sure about b). Any help and answers would be much appreciated.


View attachment 34601

View attachment 34602
Doing this in a hurry; so may not be correct. I'll use [AC] to represent vector AC, since it's hard to put the arrow on top; etc

Q1.

a) [BC] = [AC] - [AB]
b) [AD] = (1/2)([AB] + [AC])
c) [DG] = -(1/3)[AD] = -(1/6)([AB] + [AC])
d) [CG] = [AG] - [AC] = (2/3)[AD] - [AC] = (2/3)x(1/2)([AB] + [AC]) - [AC] = (1/3)[AB] - (2/3)[AC]
 

Drongoski

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Q2.

a) x.dot. (y + kz) = 0

i.e. 1x(1+k) = 2x(3+4k) = 0 ==> k = -(7/9)


b) .: vector (y + kz) is a multiple of vector x

.: i+k : 3+4k is in the same ratio as 1:2, 1 and 2 being the 2 components of vector x.

.: 3+4k = 2 x (1+k) ==> k = -(1/2)
 

Drongoski

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Basically vectors are quantities that have both magnitude and direction: like a force, velocity, acceleration or displacement. Things that have only magnitude like mass and speed are referred to as scalars. If you pick up a textbook in physics, you'll learn quite a number of the basic concepts relating to vectors.
 
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