Question

consider a vector p=i+2j+k the axis is rotated in the clockwise direction about the z axis by an angle 45'.find the vector of p?​

Answer 1

The rotation angle is positive if the rotation is in the counter-clockwise direction when viewed by an observer looking along the z-axis towards the origin. Angle units are in degrees.  When the axes are rotated through an angle 45°, the transformed equation of a curve is 17x^2 – 16xy + 17y^2 = 225. Z-axis rotation is identical to the 2D case: x' = x*cos q - y*sin q. y' = x*sin q + y*cos q.  Rotate space about the x axis so that the rotation axis lies in the xz plane. Let U = (a,b,c) be the unit vector along the rotation axis. and define d = sqrt(b2 + c2) as the length of the projection onto the yz plane. If d = 0 then the rotation axis is along the x axis and no additional rotation is necessary.