A particular point P on a rigid object has co-ordinates (x, y, z) = (2.0,2.0,0). The object is now rotated about the origin according to the Euler angles (01 , 02, 03) = (-45°, 60°, 70°) and also displaced -2.0 units along the y-axis What are the new co-ordinates of the point P?

We have two vectors A=(6.0, 9.6) and B=(-8.6, 4.4). What angle does the sum of these vectors make with the x-axis in degrees?

Deduce an expression for a rotation operation along z-axis R₂(a)= exp. La ħ

Find a unit vector perpendicular to A = (î+ ĵ – Îk) and B = ( 2i + j- 3k). (Hints. One method to find the unit vector C perpendicular to A and B will be to use the fact that the cross product is perpendicular to both vectors A and B, but keep in mind that the magnitude of the unit vector is one. There is another method which is a little bit longer by using the fact that the dot product AC=0 and BC=0 where C is the unit vector )

Jungle gym, dot products, unit vectors. A coordinate system is laid out along the bars of a large 3D jungle gym (the figure below). You start at the origin and then move according to the following steps. For each step, the distance (in meters) and direction in which you move A. are given by the cross product A x B of the given vectors A and B. For example, the first move is 18 m in the +z direction. What is the magnitude dnet of your final displacement from the origin? (a) A = 3.01, B = 6.0 (b) A = - 4.01, B = 3.0k - (c) A = 2.0₁, B = 4.0k (d) A = 3.0₁, B - 8.0 (e) A = 4.0K, B = - 2.01 (f) A = 2.01, B - 4.01

What is the angle between the vectors a = (10, -10, 0) and b = (-5, 5, 2), in radians?