Determine the position vector of ##C##

AI Thread Summary
The position vector of point C is determined to be 7i + 7j based on the calculation OC = OB + BC, where OB is 3i + 5j and BC is 4i + 2j. In part (c), the equations for point D are established using the midpoint M(4,4), leading to the coordinates x = 6 and y = 2. Part (b) confirms the vector BC as 4i + 2j, but emphasizes the need for justification through solving the equation 20 = |AB|^2 = |BC|^2. Overall, the discussion focuses on confirming the calculations and ensuring proper justification for the vector relationships.
chwala
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Homework Statement
Kindly see attached.
Relevant Equations
Vectors
Highlighted part only...

1686587242715.png


Part (a) was easy ##2\sqrt 5##.

For part (b),

...##BC=4i+2j##

it follows that,

##OC=OB+BC##

##OC=3i+5j+4i+2j=7i+7j## correct? any other better approach guys!

For part (c),

I will form the equations as follows;

Let ##D(x,y)## then,

##x-4=2(4-3)##

and

##y-4=2(4-5)## where M=##(4,4)##

##x=6, y=2##,

part (d) - Kite.
 
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For (b). you have simply asserted that BC = 4\mathrm{i} + 2\mathrm{j}. This is correct, but you need to justify it by solving <br /> 20 = |AB|^2 = |BC|^2 = (p - 3)^2 + (p - 5)^2.
 
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