7.2

Vectors

10 flashcards to master Vectors

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Key Concept Flip

Represent the displacement from point A(1, 2) to point B(4, 6) as a column vector.

Answer Flip

A column vector represents displacement. Subtract the coordinates of A from B: (4-1, 6-2) = (3, 4). Therefore, the column vector is (3, 4).

Definition Flip

Define the term 'vector' and differentiate it from a scalar.

Answer Flip

A vector is a quantity with both magnitude (size) and direction. A scalar, like temperature or mass, only has magnitude.

Key Concept Flip

Calculate the magnitude of the vector v = (5, -12).

Answer Flip

The magnitude of a vector (x, y) is √(x² + y²). For v = (5, -12), the magnitude is √(5² + (-12)²) = √(25 + 144) = √169 = 13.

Key Concept Flip

If vector a = (2, -1) and vector b = (-3, 4), find the resultant vector a + b.

Answer Flip

To add vectors, add their corresponding components. a + b = (2 + (-3), -1 + 4) = (-1, 3).

Definition Flip

Explain the concept of a 'position vector'.

Answer Flip

A position vector describes the location of a point relative to the origin (0,0).

Example: the position vector of point (3,5) is (3,5).
Key Concept Flip

Vectors p and q are parallel. If p = (2, -3), give a possible vector for q and explain your reasoning.

Answer Flip

Parallel vectors are scalar multiples of each other. q could be (4, -6) because q = 2 * p. Both vectors have the same direction.

Key Concept Flip

Describe how to perform vector subtraction, a - b, geometrically.

Answer Flip

Geometrically, a - b is equivalent to a + (-b). You reverse the direction of vector b and then add it to vector a using the parallelogram or triangle rule.

Key Concept Flip

Vector 'r' is the scalar multiple 3 * (1, -2). Determine vector r.

Answer Flip

To find the scalar multiple, multiply each component of the vector by the scalar. r = (3*1, 3*-2) = (3, -6).

Definition Flip

What does it mean for two vectors to be 'equal'?

Answer Flip

Two vectors are equal if and only if they have the same magnitude and the same direction (or, equivalently, the same components).

Key Concept Flip

Explain what a 'negative vector' is, using vector a = (4,1) as an example.

Answer Flip

A negative vector has the same magnitude but the opposite direction. The negative vector of a = (4, 1) is -a = (-4, -1).

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7.1 Transformations 8.1 Basic probability

Key Questions: Vectors

Define the term 'vector' and differentiate it from a scalar.

A vector is a quantity with both magnitude (size) and direction. A scalar, like temperature or mass, only has magnitude.

Explain the concept of a 'position vector'.

A position vector describes the location of a point relative to the origin (0,0).

Example: the position vector of point (3,5) is (3,5).
What does it mean for two vectors to be 'equal'?

Two vectors are equal if and only if they have the same magnitude and the same direction (or, equivalently, the same components).

About Vectors (7.2)

These 10 flashcards cover everything you need to know about Vectors for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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