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C4 vector question

Q: Given that the points A and B have co-ordinates (7, 4, 4) and (2, -2, -1) respectively, use a vector method to find the value of Cos AOB, where O is the origin. Prove that the area of triangle AOB is 5292 \frac{5 \sqrt29}{2}

I have got the value for Cos AOB which is 227 \frac{2}{27}

But any tips on how to go about doing the second part? I haven't touched C4 since July so I'm a bit rusty.

I was thinking maybe drawing a triangle with the x, y co-oridnates but I believe that won't work and I must consider the z value too! And, what can I do with the Cos AOB...I was thinking maybe get the sine value for that angle and put into the area of triangle formula but I think I have gone wrong somewhere.

EDIT: Ooh by drawing a triangle I can see that the Sin AOB will be 52927 \frac{5 \sqrt29}{27} but now what? :confused:
Reply 1
Well, the area of the triangle = 0.5|OA||OB|sin(AOB), so you're almost there :smile: .
n_251
Q: Given that the points A and B have co-ordinates (7, 4, 4) and (2, -2, -1) respectively, use a vector method to find the value of Cos AOB, where O is the origin. Prove that the area of triangle AOB is 5292 \frac{5 \sqrt29}{2}

I have got the value for Cos AOB which is 227 \frac{2}{27}

But any tips on how to go about doing the second part? I haven't touched C4 since July so I'm a bit rusty.

I was thinking maybe drawing a triangle with the x, y co-oridnates but I believe that won't work and I must consider the z value too! And, what can I do with the Cos AOB...I was thinking maybe get the sine value for that angle and put into the area of triangle formula but I think I have gone wrong somewhere.

EDIT: Ooh by drawing a triangle I can see that the Sin AOB will be 52927 \frac{5 \sqrt29}{27} but now what? :confused:


Area of a triangle ABC, = 12absinC\frac{1}{2}absin C
Reply 3
Simba
Well, the area of the triangle = 0.5|OA||OB|sin(AOB), so you're almost there :smile: .


Ahh I can't believe it! :eek3:

Thanks so much!
Reply 4
namedeprived
Area of a triangle ABC, = 12absinC\frac{1}{2}absin C


:yes: Yup I had that but I kept on working in two dimensions...I needed to consider the k vector too! Thanks!

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