# Further maths vectors questionWatch

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#1
Q) Two sloping roof structures must be constructed at an angle of 60°. The roof structures can be modelled as planes given by the equations
x+2y+2z=5
ax+y+z=2

Find the exact value of a.

I'm not sure how to do this question. I tried using the dot product of the direction vectors (1,2,2) and (a,1,1) but ended up with a polynomial that lacked real roots. Any help would be appreciated
0
3 weeks ago
#2
(Original post by theeetimdoherty)
Q) Two sloping roof structures must be constructed at an angle of 60°. The roof structures can be modelled as planes given by the equations
x+2y+2z=5
ax+y+z=2

Find the exact value of a.

I'm not sure how to do this question. I tried using the dot product of the direction vectors (1,2,2) and (a,1,1) but ended up with a polynomial that lacked real roots. Any help would be appreciated
Perhaps post your derivation of the polynomial?
0
3 weeks ago
#3
(Original post by theeetimdoherty)
Q) Two sloping roof structures must be constructed at an angle of 60°. The roof structures can be modelled as planes given by the equations
x+2y+2z=5
ax+y+z=2

Find the exact value of a.

I'm not sure how to do this question. I tried using the dot product of the direction vectors (1,2,2) and (a,1,1) but ended up with a polynomial that lacked real roots. Any help would be appreciated
This question reminds me of matrices and how they can represent planes forming a prism...as they have to be at an angle of 60 degrees
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