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Original
2026-01-01
Modified
2026-02-28
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<p><strong>Zero Vector</strong></p>
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<p><strong>Zero Vector</strong></p>
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<p>Definition: The zero vector has a magnitude of zero with no specific direction. Notation: 0 Example: \(0 = 0i + 0j + 0k\)</p>
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<p>Definition: The zero vector has a magnitude of zero with no specific direction. Notation: 0 Example: \(0 = 0i + 0j + 0k\)</p>
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<p><strong>Unit Vector </strong></p>
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<p><strong>Unit Vector </strong></p>
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<p>Definition: We use this to indicate direction, and a unit vector has a magnitude of 1. Notation: A Example: For \(A = 3i +4j, A = 32 + 42 = 25 = 5\)</p>
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<p>Definition: We use this to indicate direction, and a unit vector has a magnitude of 1. Notation: A Example: For \(A = 3i +4j, A = 32 + 42 = 25 = 5\)</p>
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<p><strong>Position Vector </strong></p>
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<p><strong>Position Vector </strong></p>
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<p>Definition: A position vector shows the location of a point in space relative to the origin. It shows the arrow pointing from the origin to the point. Notation: r Example: The position vector of a point P(x, y, z) is \(r = xi + yj + zk \)</p>
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<p>Definition: A position vector shows the location of a point in space relative to the origin. It shows the arrow pointing from the origin to the point. Notation: r Example: The position vector of a point P(x, y, z) is \(r = xi + yj + zk \)</p>
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<p><strong>Co-initial Vectors</strong></p>
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<p><strong>Co-initial Vectors</strong></p>
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<p>Definition: They have the same initial point, even if they point in different directions or have different magnitudes. Example: If Vector A and Vector B both start from the origin (0, 0) but point in different directions, then they’re<a>co-initial vectors</a>. </p>
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<p>Definition: They have the same initial point, even if they point in different directions or have different magnitudes. Example: If Vector A and Vector B both start from the origin (0, 0) but point in different directions, then they’re<a>co-initial vectors</a>. </p>
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<p><strong>Collinear Vector</strong></p>
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<p><strong>Collinear Vector</strong></p>
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<p>Definition: These lie near the same line or are parallel to each other. Example: \(A = 2i + 3j\) and \(B = 4i + 6j\) are collinear.</p>
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<p>Definition: These lie near the same line or are parallel to each other. Example: \(A = 2i + 3j\) and \(B = 4i + 6j\) are collinear.</p>
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<p><strong>Equal Vector</strong> </p>
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<p><strong>Equal Vector</strong> </p>
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<p>Definition: These have the same magnitude and directions at any point of their initial points. Example: \(A = 3i + 4j and B = 3i + 4j\)</p>
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<p>Definition: These have the same magnitude and directions at any point of their initial points. Example: \(A = 3i + 4j and B = 3i + 4j\)</p>
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<p><strong>Negative of a Vector</strong></p>
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<p><strong>Negative of a Vector</strong></p>
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<p>Definition: This has the same magnitude as a given vector but points in the opposite direction. Example: If \(A = 5i + 2j\), then the negative of vector A is: \(-A = -5i - 2j\)</p>
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<p>Definition: This has the same magnitude as a given vector but points in the opposite direction. Example: If \(A = 5i + 2j\), then the negative of vector A is: \(-A = -5i - 2j\)</p>
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<p><strong>Parallel Vectors </strong></p>
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<p><strong>Parallel Vectors </strong></p>
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<p>Definition: Parallel vectors have the same or exactly opposite direction. They may have different magnitudes, but their directions are aligned. Example: Vector A and KA, where k is a scalar, are parallel.</p>
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<p>Definition: Parallel vectors have the same or exactly opposite direction. They may have different magnitudes, but their directions are aligned. Example: Vector A and KA, where k is a scalar, are parallel.</p>
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<p><strong>Orthogonal Vectors</strong></p>
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<p><strong>Orthogonal Vectors</strong></p>
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<p> Definition: These vectors are perpendicular to each other, meaning they form a 90o degree angle when they intersect. Example: If \(A = i + 2j\) and \(B = -2i + j\), then \(AB = 0\).</p>
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<p> Definition: These vectors are perpendicular to each other, meaning they form a 90o degree angle when they intersect. Example: If \(A = i + 2j\) and \(B = -2i + j\), then \(AB = 0\).</p>
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<p><strong> Coplanar Vector</strong></p>
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<p><strong> Coplanar Vector</strong></p>
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<p>Definition: This lies in the same plane. Example: Vectors \(A = 2i + 3j\) and \(B = -i + 4j\) are coplanar with any vector in the xy-plane. </p>
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<p>Definition: This lies in the same plane. Example: Vectors \(A = 2i + 3j\) and \(B = -i + 4j\) are coplanar with any vector in the xy-plane. </p>
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