The base of the roof, 𝑂𝐴𝐵𝐶, is rectangular and horizontal with 𝑂𝐴 = 𝐶𝐵 = 14 𝑚 and 𝑂𝐶 = 𝐴𝐵 = 8 𝑚. The top of the roof 𝐷𝐸 is 5 𝑚 above the base and DE = 6m. The sloping edges 𝑂𝐷,𝐶𝐷,𝐴𝐸 and 𝐵𝐸 are all equal in length.

Question

Unit vector i and j are parallel to OA and OC respectively and the unit vectors k is vertically upwards.
(i) Express the vector 𝑂𝐷⃗⃗⃗⃗⃗⃗ in terms of i , j and k, and find its magnitude (4 marks)
(ii) Use a scalar product to find angle 𝐷𝑂𝐵. (5 marks)

Answer 1

was there something wrong with the solution I gave you earlier?

www.jiskha.com/questions/1884051/the-base-of-the-roof-is-rectangular-and-horizontal-with

Answer 2

sorry about that. I forgot you had answered the question.
Could you go a bit more in-depth with (ii) because I haven't done vectors before.

Answer 3

OD = 4i+4j+4k
OB = 14i+8j
If θ = ∡DOB, then
OB•OD = |OB| * |OD| cosθ

OB•OD = 4*14 + 4*8 + 4*0 = 88
|OD| = √(4^2+4^2+4^2) = 4√3
|OB| = √(14^2+8^2) = 2√65
so,
cosθ = 88/(4√3 * 2√65) = 0.7877
θ = 38°