Hello, please help me with this math question. Topic: VECTORS. Level: 1st year at University, Mathematics 1.

Consider r(t) = the position vector of a particle at time t ∈ [0, 30], where the components of r are expressed in centimeters and time in seconds. Let vector OP be the position vector of the particle after 1 sec.

a. Show that all vectors PQ, where Q(x, y, z) is an arbitrary point, orthogonal to the instantaneous velocity vector v(1) of the particle after 1 sec, can be expressed as PQ = , where xsin1 - ycos1 - 2z + 4 = 0. The set of point Q describes a plane called the normal plane to the path of the particle at point P.

The original exercise is included as a picture!

I've been trying to get this right but failed so far. I still have a couple of hours to get it done though. Thank you so much for your help!!!