Assignment:
Q1. Find the angle between the planes with the given equations.
2x – y + z = 5 and x + y – z = 1
Q2. Find the values of r’ (t) and r’’ (t) for the given values of t.
r (t) = i cos t + j sin t; t = π/4
Q3. The acceleration vector a (t), the initial position r0 = r (0), and the initial velocity v0 = v (0) of a particle moving in xyz- space are given. Find its position vector r (t) at time t.
a(t) = 6ti – 5j + 12t²k; r0 = 3i + 4j; v0 = 4j – 5k
Q4. Find the curvature of the given plane curve at the indicated point.
x = t – 1, y = t² + 3t + 2, where t = 2
Q5. Find the unit tangent and normal vectors at the indicated point.
x = t³, y = t² at (-1, 1)
Provide complete and step by step solution for the question and show calculations and use formulas.