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csi

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Hi guys,

That attached are some questions that I need help with. The answers printed in small font on the bottom right hand side of each question (the answer for the last question got cut off, it’s meant to be 1/2)

Many thanks:)
 

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zerdaunal1

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Hi guys,

That attached are some questions that I need help with. The answers printed in small font on the bottom right hand side of each question (the answer for the last question got cut off, it’s meant to be 1/2)

Many thanks:)
Hii, for the first part, instead of evaluating AB, try using the midpoint formula for vectors OA and OB, this gives you the answer you need.

for ii) vector CM = OM-OC (we just found OM and already are given OC)

for iii, we find the magnitude for both OM and CM, equate it to one another (given) and then expand and solve for k

for iii)
We know that collinearity refers to the direction of the vectors (relative to x-axis) are equal. Consider how to compute the direction of a vector and choose two vectors for example OA and AB, find their direction and equate them, once you’ve done this you can solve for k. (Check attached file)
p.s sorry for the messy handwriting, hope this helps :)
 

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CM_Tutor

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We are given that:
  • is the midpoint of
Part (a)



Now, as is the midpoint of , and . Thus,



and so



Part (b)



Part (c)



So, since we are given that , the only solution to is .

Part (d)

We already know that , , and , are collinear as is the midpoint of and must lie on . If also lies on this line, then there must be some constant such that :



Equating the and components, we see that



and then that



is the required value of for to lie on the line that includes , , and , and thus that these four points are collinear.

Note that the same result, , could be obtained with other combinations of vectors (which would then yield different values of ), including
 
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CM_Tutor

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Question 2

We are given that:
  • , , and are collinear

For to lie on , there must be some constant such that :







Equating the and components, we see that



and then that



is the required value of for to lie on the line that includes and .
 
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csi

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Question 2

We are given that:
  • , , and are collinear

For to lie on , there must be some constant such that :







Equating the and components, we see that



and then that



is the required value of for to lie on the line that includes and .
tysm
 

csi

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Hii, for the first part, instead of evaluating AB, try using the midpoint formula for vectors OA and OB, this gives you the answer you need.

for ii) vector CM = OM-OC (we just found OM and already are given OC)

for iii, we find the magnitude for both OM and CM, equate it to one another (given) and then expand and solve for k

for iii)
We know that collinearity refers to the direction of the vectors (relative to x-axis) are equal. Consider how to compute the direction of a vector and choose two vectors for example OA and AB, find their direction and equate them, once you’ve done this you can solve for k. (Check attached file)
p.s sorry for the messy handwriting, hope this helps :)
ty!!
 

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