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MAT1503 Assignment 4 Memo | Due 29 August 2025. Step-by-Step Calculations Provided. Question 1 (1.1) Find an equation for the plane that passes through the origin (0, 0, 0) and is parallel to the plane −x + 3y − 2z = 6. (1.2) Find the distance between the point (−1,−2, 0) and the plane 3x − y + 4z = −2. Question 2: 15 Marks (2.1) Find the angle between the two vectors ⃗v = ⟨−1, 1, 0,−1⟩ ⃗v = ⟨1,−1, 3,−2⟩. Determine (3) whether both vectors are perpendicular, parallel or neither. (2.2) Find the direction cosines and the direction angles for the vector ⃗r = ⟨0,−1,−2, 3 4 ⟩. (2.3) HMW:Additional Exercises. Let ⃗r (t) = ⟨t,−1t , t2 − 2⟩. Evaluate the derivative of ⃗r (t)|t=1 . Calculate the derivative of V(t) · ⃗r (t) whenever V(1) = ⟨−1, 1,−2⟩ and V′(1) = ⟨1,−2, 2⟩.
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