Final answer:
Angular displacement and velocity are vector quantities, which means they have both magnitude and direction, making the statement true. Centripetal acceleration is also a vector because it has a direction in addition to magnitude. The resultant vector's magnitude and direction can indeed be determined from component vectors.
Step-by-step explanation:
The statement about angular displacement and velocity is true; they are indeed vector quantities. This means that both include a magnitude and a direction. Angular displacement describes the angle through which a point or line has been rotated in a specified sense about a specified axis. Angular velocity, on the other hand, describes how rapidly the angular displacement is changing with time. Velocity always incorporates direction, which is why it is a vector quantity. For example, angular velocity is usually denoted by the symbol \( \omega \) and is given as a vector that points along the axis of rotation according to the right-hand rule.
To answer part of your question, 'c. Vector quantity; centripetal acceleration has magnitude only but no direction' is not correct. Centripetal acceleration is indeed a vector because it also has a direction towards the center of the circular path.
In response to the question regarding the resultant vector, it is true that we can find the magnitude and direction of the resultant vector if we know the angles and magnitude of two vectors. Moreover, the direction of the resultant vector does indeed depend on both the magnitude and direction of the combined vectors, making statement 37 also true. Additionally, vectors in a plane can be decomposed into components and can thereby form the shape of a right triangle, so statement 60 is also true.
Regarding the vectors and scalar question, the correct combination that includes two vectors and one scalar is 'b. displacement, velocity, acceleration,' since distance and speed are scalar quantities, while displacement and velocity are vectors.