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OCR A-level Maths Basics of vectors

Basics of vectors

This page covers the following topics:

Vector is a quantity with both a magnitude and a direction. In textbooks, vectors are denoted by a BOLD letter such as v. As it is hard to write bold letters in pen or paper, written work often uses different notation such as v, v, arrow or AB(arrow). The order of letters and arrows in the last example is important - in this case it tells us that the vector is going from point A to point B.

Vector basics

Column notation (column vectors) and horizontal bracket notation (row vectors) can be used to express vectors. Horizontal bracket notation has no commas between the components, and should not be confused with coordinates.

Column vectors

To obtain the vector expression/equation, assume that the starting point of the vector is placed at the origins of an axes with labels i, j, k (you may consider them to be equivalent to x y and z axes). The vector equation is then given by how far along the vector goes with respect to these axes.

Cartesian coordinates

Unit vectors are vectors that have a magnitude of 1, no matter the direction. Often, they are used to denote axes. A unit vector can be obtained by dividing a given vector by its magnitude.

Unit vectors

Equal vectors are vectors which have the same magnitude and direction, regardless of where they are located. Say we have a vector r, then the negative vector βˆ’r has the same magnitude as r, but points in the opposite direction.

Equal vectors

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A vector is 4 units in x direction, negative 6 units in y direction and 7 units in z direction. What is a column notation for this vector?

OCR A-level Maths Basics of vectors A vector is 4 units in x direction, negative 6 units in y direction and 7 units in z direction. What is a column notation for this vector?
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2

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A shop is 30 meters south and 20 meters west from Catherine’s house. Provide a vector for the path Catherine has to take to get to the shop from her home. Give your answer as a column vector.

OCR A-level Maths Basics of vectors A shop is 30 meters south and 20 meters west from Catherine’s house. Provide a vector for the path Catherine has to take to get to the shop from her home. Give your answer as a column vector.
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3

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Consider the vector shown. Which vector equation correctly describes the vector?

OCR A-level Maths Basics of vectors Consider the vector shown. Which vector equation correctly describes the vector?
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4

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Consider the vectors shown. What is the vector equation for vector c)?

OCR A-level Maths Basics of vectors Consider the vectors shown. What is the vector equation for vector c)?
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5

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Consider a unit cube. A vector which starts at the bottom left corner on the near face has it's other end at the top right corner in the far face. What is the vector equation for this vector?

OCR A-level Maths Basics of vectors Consider a unit cube. A vector which starts at the bottom left corner on the near face has it's other end at the top right corner in the far face. What is the vector equation for this vector?
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6

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Calculate the vector equation for a unit vector in the same direction as vector v = 3i + 4j.

OCR A-level Maths Basics of vectors Calculate the vector equation for a unit vector in the same direction as vector v = 3i + 4j.
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7

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A vector is 12 units in x direction and negative 5 units in y direction. What would be the Cartesian equation for a unit vector going in the same direction?

OCR A-level Maths Basics of vectors A vector is 12 units in x direction and negative 5 units in y direction. What would be the Cartesian equation for a unit vector going in the same direction?
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8

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What is the equation for a unit vector going in the same direction as the vector shown?

OCR A-level Maths Basics of vectors What is the equation for a unit vector going in the same direction as the vector shown?
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