Question

3. X is an unknown vector satisfying the following two relations involving the known vectors N and V and the known scalar : Ñ X X = Ñ X = 0 Derive a vector (not vector component) expression for X in terms of Ñ, V, o, and N, the magnitude of N. Hint: Draw all three vectors with a common base point, starting with N drawn in the vertical direction. What does the first relation above imply about the direction of V with respect to Ñ?

the furthest i could get is that the dot product between vector N and vector V, as well as vector X and vector V must be zero but that's about it. I get stuck when trying to use the cosine relation with the dot product but since the question doesn't allow me to write it in terms of an angle, i can't really use that. If someone could show me how this would help incredibly!

Answer 1

Soli Given two relations are Ñ Ñ ñ .- NON-0---(2) where N , W and of are known. Now if we drais Ñ with respect to a base point say o in vertical direction in the plane of 0 as below: then since iga vector, which is same with the cross product of N and another vector X, we must have to consider in the perpendicular direction of the plane containing the rector. Nas below: ne., Novo In other way since Ñ. (N x V) - Ñ Ñ V 7.0 so we must have Novoo, otherwise eg. I will be inconsistent. 7

I of eq. (1) or becomes inconsistent, then there is no solution for a 1 So for Nov = 0 and ñ to, then eg. (1) implies, | Nxxxx VN > PX - CNTT NVX => N2 - I Ñ - JxX (Using (²) Y Y = 1 (JxX+6N) this is the requirred solution If N 2 8 , then there is no colection unless J and 6=0 and in that case y can be any arbitrary vector.