D is 4m in from AC, so
OD = 4i+4j+4k
OB = 14i+8j
If ΞΈ = β‘DOB, then
OBβ’OD = |OB| * |OD| cosΞΈ
I assume you know how to find the dot product and magnitudes
The base of the roof, ππ΄π΅πΆ, is rectangular and horizontal with ππ΄ = πΆπ΅ = 14 π and ππΆ = π΄π΅ = 8 π. The top of the roof π·πΈ is 5 π above the base and DE = 6m. The sloping edges ππ·,πΆπ·,π΄πΈ and π΅πΈ are all equal in length.
Unit vector i and j are parallel to OA and OC respectively and the unit vectors k is vertically upwards.
(i) Express the vector ππ·ββββββ in terms of i , j and k, and find its magnitude (4 marks)
(ii) Use a scalar product to find angle π·ππ΅. (5 marks)
1 answer