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Maths

Vectors - Higher

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A vector describes a movement from one point to another.

Vector notation

A vector quantity has both direction and magnitude (size).

(In contrast a scalar quantity has magnitude only - eg, the numbers 1, 2, 3, 4...)

image: a grid with a diagonal line marked A and B at each respective end. There's an arror in the centre pointing in the upward direction labelled a.

For example this arrow represents a vector. The direction is given by the arrow, while the length of the line represents the magnitude.

This vector can be written as: AB (arrow above) , a, or 3 over 4 .

In print, a is written in bold type. In handwriting, the vector is indicated by putting a squiggle underneath the letter: the letter with a squiggle underneath it indicating a vector

Question

Write down the 3 ways to describe the vector if the arrow is now pointing from B to A.

image: a grid with a diagonal line marked A and B at each respective end. There's an arror in the centre pointing in the downward direction

Answer

Remember that the arrow describes the direction. So, in this case, the vector is from B to A. If we move 'backwards' along a vector, it becomes negative, so a becomes -a. Moving from B to A entails moving 3 units to the left, and 4 down.

So the three ways to write this vector are:

BA (arrow above) , -a and -3 over -4

image: two parallel lines at a diagonal angle, on the left line an arrow points in an upward direction and is labelled a, on the right line an arrow points in the downward direction and is labelled minus a

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