Assignment IR & AI PDF

[Assignment] **Q1)** A vector is described as P=3i+5j+2k. Express the vector in matrix form: 1\) With a scale factor of 2 2\) If it were to describe a direction as a unit vector **Q2)** A vector p is 5 units long and is in the direction of a unit vector q described as follows. Express the vecto...

[Assignment] **Q1)** A vector is described as P=3i+5j+2k. Express the vector in matrix form: 1\) With a scale factor of 2 2\) If it were to describe a direction as a unit vector **Q2)** A vector p is 5 units long and is in the direction of a unit vector q described as follows. Express the vector in matrix form. **Q3)** For the following frame, find the values of the missing elements and complete the matrix representation of the frame:  **Q4)** Find the missing elements of the following frame representation: **Q5)** A frame F is moved 3 units along the x-axis and 2 units along the z-axis of the reference frame. Find the new location of the frame.  **Q6)** A point p\[2, 3, 4\]^T^ is attached to a rotating frame. The frame rotates 90∘ about the x-axis of the reference frame. Find the coordinates of the point relative to the reference frame after the rotation. **Q7)** A point p\[7, 3, 1\]^T^ is attached to a frame Fnoa and is subjected to the following transformations: 1\) Rotation of 90∘ about the z-axis 2\) Followed by a rotation of 90∘ about the y-axis 3\) Followed by a translation of \[4, −3, 7\] Find the coordinates of the point relative to the reference frame at the conclusion of transformations. **Q8)** Compute the homogeneous transformation representing a translation of 3 units along the x-axis and followed by rotation of 900 about the current z-axis followed by a translation of 1 unit along the fixed y-axis **Q9)** A 3-DOF robot arm has been designed for applying paint on flat walls, as shown. Assign coordinate frames as necessary based on the D-H representation. Fill out the parameters table. **Q10)** Consider the three-link planar manipulator shown in Figure. Derive the forward kinematic equations using the DH-convention.  **Q11)** Compute the truth table of **Q12)** Translate the following Propositional Logic to English sentences. Let: E=Liron is eating H=Liron is hungry   **Q13)** Use the truth tables method to determine whether is valid. **Q14)** P(x) : "x + 2 = 5, universe of discourse: {1, 2, 3}.  , are true or false. Proove it. **Q15)** Use the truth tables method to determine whether are logically equivalent.