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2D vectors for SQA Higher Maths

2D vectors

This page covers the following topics:

1. Adding 2D vectors
2. Subtracting 2D vectors
3. Multiplying 2D vectors
4. Magnitude of 2D vectors
5. Proof with 2D vectors

2D vectors are added by adding their corresponding coordinates or by connecting them โ€œhead to toeโ€.

Adding 2D vectors

To subtract 2D vectors, reverse the direction of the vector that is subtracted or subtract corresponding coordinates.

Subtracting 2D vectors

Two vectors can be multiplied by using a dot product, which can be obtained by multiplying corresponding coordinates and adding the results up. Alternatively, cosine value of an angle between the vectors may be used.

Multiplying 2D vectors

The magnitude of a 2D vector is found using Pythagoras' theorem for a right angle triangle, given by M = โˆš(aยฒ + bยฒ).

Magnitude of 2D vectors

If vectors are multiples of each other, they are parallel to each other.

Proof with 2D vectors

1

What is the magnitude of vector c shown in the figure?

7.5

What is the magnitude of vector c shown in the figure?

2

Find a โˆ’ b if a = 4i + 7j and b = 3i โˆ’ 2j.

i + 9j

Find a โˆ’ b if a = 4i + 7j and b = 3i โˆ’ 2j.

3

P is a point on AB such that AP : PB = 1 : 4. Find OP.

OP = 0.8a + 0.2b

P is a point on AB such that AP : PB = 1 : 4. Find OP.

4

A boat sails north for 30 km. Finally, it travels 10 km due south before arriving at its destination. Find the magnitude of the vector connecting the start point to the end point.

20 km

A boat sails north for 30 km. Finally, it travels 10 km due south before arriving at its destination. Find the magnitude of the vector connecting the start point to the end point.

5

Find the magnitude of the vector u if u = (2 6).

2โˆš10

Find the magnitude of the vector u if u = (2 6).

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