MAT1503 ASSIGNMENT 4 2025 – STEP-BY-STEP CALCULATIONS PROVIDED (DUE 29 AUGUST 2025)

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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⟩.