SQA Higher- Vectors

I just cannot understand this question but i know the answer is (-5,-5, 7) I really want to how it's done, this is the question:

VABCD is a pyramid with the rectangle base ABCD The vectors of AB , AD and AV are given by: AB = 8i+2j+2k AD=-2i+10j - 2k AV= i +7j +7k

Express CV in component form ?

Help will be greatly appreciated

Answers
When you say you don't understand the question, is it the background you are having difficulty with, or the mechanism of interpreting it?If you were to draw a set of orthogonal axes, called i, j and k, then  you could have A and B as two points in this i-j-k space.  Then it would make sense to say AB = 8i+2j+2k.  If you started at A, and went 8 units in the i direction, 2 units in the j direction, and 2 units in the k direction, then you'd be at B.  I'd recommend trying a few simple examples in 2 dimensions to get the hang of it and then extend the procedure to 3.  You can draw out examples in 2 dimensions and check your results by measuring your diagram.  It's a bit more tricky in 3 dimensions.If you are OK with the idea behind the geometry, then define A as the point 0,0,0 and then you have the coordinates of B, D and V.  You know that ABCD is a rectangle so you should be able to calculate the coordinates of C.  (from A,B and D)  If you know C's coordinates then you can go on to find the translation that would take one from C to V.
ianmoth
23 February 2014
To see this work, draw a rectangular based pyramid and label it as described - VABCD. Draw in your given vectors.You can then see that CV = CB + BA + AV     = - AD - AB + AV= - ( - 2i + 10j - 2k) - (8i +2j + 2k) + (i + 7j + 7k)= 2i - 10j +2k - 8i -2j - 2k + i + 7j + 7k= - 5i -5j +7kSo the components of CV are ( -5, -5, 7)Hope this helps :)
cajones
01 March 2014
We have: AC=AB+AD = 6i+12jIn addition: CV=AV-AC= (i+7j+7k) - (6i+12j) = -5i-5j+7k
harry_dinh
09 March 2014
Thank you both for replying and I'm sorry that i didn't reply sooner but somehow, i wasn't notified of your responses. This helped a lot, thank you so much .
milkyall
31 March 2014
You're welcome :)
cajones
01 April 2014
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