maths a2 vectors question

parallelogram PQRS.
Given that PQ=i+10j-3k and QR=8i+3j+2k, find the area of the quadrilateral, to one decimal place. (6 marks) (from Edexcel practice book)
I am getting 92.0, but the answer is 86.3. I just did the modulus of both then times them together? Seems like that way isn't correct.
Does anyone know how to tackle this problem?

If you multiplied, that would assume it's a rectangle?
How to adapt for a parallelogram?

Is the book for the current a-level (further)?

yes current a level maths
image is attached QUESTION 6

Ok so what is the area of a parallelogram?

Oh base times VERTICAL height. ok let me try it again.

Yes, you'll need the angle between the vectors to get the vertical height.
Have you done the dot product (further)?

yes, doing year 1 further. Ok ill try that. Shouldnt there be another way as this question isnt further?

yes, doing year 1 further. Ok ill try that. Shouldnt there be another way as this question isnt further?

yes, doing year 1 further. Ok ill try that. Shouldnt there be another way as this question isnt further?

got 68.6 degrees. Then what?

parallelogram PQRS.
Given that PQ=i+10j-3k and QR=8i+3j+2k, find the area of the quadrilateral, to one decimal place. (6 marks) (from Edexcel practice book)
I am getting 92.0, but the answer is 86.3. I just did the modulus of both then times them together? Seems like that way isn't correct.
Does anyone know how to tackle this problem?

I may be wrong but I wouldn't expect to see a question like this in the final exam because the further maths dot product method is the quicker approach (cross product is even faster if you do further pure). A Level maths questions are normally designed so that on spec methods are the quickest and most efficient.

I am in complete agreement with you but the practice book that he is using is based on the new spec so there must be something with that question that we are missing

I posted a way to do it without further maths methods above. It just involves simple GCSE trig.

i am bored so here it is...
screen shot at 48 give an idea of the method,
screenshot at 50 helps with multiplication

nah that method gave me 85.68

cause 1^2 +10^2+3^2=110
and 8^2+3^2+2^2=77
and theta is 68.6 from above
using |a||b|*sin(theta)=85.68
something is off