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There are a few problems regarding vectors which I am not sure on how to go about solving them. These problems are listed below along with my working.

_____________________________________ Find the vector equation of the circle centre C, position vector -7i+4j, and a radius of [tex]4\sqrt{5}[/tex] units. Determine wether the point A, position vector i+8j, lies inside, on or outside the circle.

My working:

Vector equation:

[tex]\mid{r - (-7i + 4j)}\mid = 4\sqrt{5}[/tex]

[tex]\mid{r + 7i - 4j}\mid=4\sqrt{5}[/tex]

As for the second part I have used the vector equation and substituted r with vector a

[tex]\mid{(i+8j)+(7i-4j)}\mid = 4\sqrt{5}[/tex]

[tex]\mid{8i+5j}\mid <> 4\sqrt{5}[/tex]

(<> means does not equal, I don’t know the latex code)

However on the answers it says that this point does lie on the circle, so I know I’m wrong but don’t know where or why.

_____________________________________ Find the distance between the centres of the two circles given below

[tex]\mid{r - (3i+7j)}\mid = 6[/tex]

[tex]\mid{r-2i - 9j}\mid = 7[/tex]

As for this problem I don’t know where to start.

_____________________________________ The circle [tex]\mid{r – (3i – 4j)\mid =5[/tex] has the centre A and [tex]\mid{r – (2i + 7j)}\mid = 3[/tex] has the centre B. Find the euation of the straight line A and B.

Again this is another problem which I’m unaware on how to approach

_____________________________________ thank you to people who post a reply, and even hints are appreciated for the problems which I do not know how to solve

Pavadrin

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# Vector Equation of a line

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