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EDEXCEL FP3 VECTORS (book exam style paper)

I have solved parts a and b,

I would like some help with part c. if someone could please explain the method into working out part c.

QUESTION AND SOLUTIONS IS IN ATTACHMENT BELOW PLEASE CHECK!


I do not understand the middle line of the working out of part c, where the vectors are multiplied and divided by the modulus.
Can someone explain how the values in the denominator for working out modulus is done please, I do not understand the why -8 is multiplied by 2, and why -4 is multiplied by 2 either. and also how the 92 comes about.

THANKS IN ADVANCE!
Original post by Coral Reafs
I have solved parts a and b,

I would like some help with part c. if someone could please explain the method into working out part c.

QUESTION AND SOLUTIONS IS IN ATTACHMENT BELOW PLEASE CHECK!


I do not understand the middle line of the working out of part c, where the vectors are multiplied and divided by the modulus.
Can someone explain how the values in the denominator for working out modulus is done please, I do not understand the why -8 is multiplied by 2, and why -4 is multiplied by 2 either. and also how the 92 comes about.

THANKS IN ADVANCE!


It says

(8)2+(4)2+92\sqrt{(-8)^2+(-4)^2+9^2}
Original post by TenOfThem
It says

(8)2+(4)2+92\sqrt{(-8)^2+(-4)^2+9^2}


oo it's square, it didn't show the indices properly on the CD.

Also, could you explain the middle line of working to me please?

thank you!
Original post by Coral Reafs
oo it's square, it didn't show the indices properly on the CD.

Also, could you explain the middle line of working to me please?

thank you!


(1,-1,4) is a vector from the point to the plane

Then (-8,-4,9)is divided by it's magnitude to give n^

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