EC3202 – Engineering
Electromagnetics
Tutorial 1 – Vector Algebra
2
Problem 1
 Vector A starts at (1, -1, -2) and ends at point (2, -1, 0). Find a unit vector in
the direction of A.
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Problem 2
 Given vectors A = 2ො𝐱 - 3𝐲ො + 𝐳ො, B = 2ො𝐱 - 𝐲ො + 3ො𝐳, and C = 4ො𝐱 + 2𝐲ො - 2ො𝐳; show that
C is perpendicular to both A and B.
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Problem 3
 In Cartesian coordinates, the three corners of a triangle are P1(0, 2, 2), P2(2,
-2, 2) and P3(1, 1, -2). Find the area of the triangle.
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Problem 4
 Given A = 2ො𝐱 - 3𝐲ො + 𝐳ො, and B = Bx𝐱ො + 2𝐲ො + Bz𝐳ො,
 (a) Find Bx and Bz, if A is parallel to B
 (b) Find a relationship between Bx and Bz, if A is perpendicular to B
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Problem 5
 Given A = (2x + 3y)ො𝐱 - (2y + 3z)𝐲ො + (3x – y)ො𝐳, determine a unit vector parallel
to A at point P(1, -1, 2).
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