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Working with vectors for SQA Higher Maths

Working with vectors

This page covers the following topics:

1. Component form of vectors

If given the angle the vector makes with the x or y axis and the magnitude of the vector, we can work out the vector equations using trigonometry (SOHCAHTOA).

Component form of vectors

1

What is the y component of a vector that has a magnitude of 50 which makes a 20ยบ angle with the x axis?

17

What is the y component of a vector that has a magnitude of 50 which makes a 20ยบ angle with the x axis?

2

Find a vector opposite to the one shown in the diagram. Give your answer as a row vector rounding each coordinate to integers.

v = (โˆ’7 โˆ’4)

Find a vector opposite to the one shown in the diagram. Give your answer as a row vector rounding each coordinate to integers.

3

An airplane travels at a speed of 100 km/h due north. Winds of 40 km/h travelling due west hit the airplane. What is the new angle the airplane travels in, with respect to the north?

21.8ยฐ

An airplane travels at a speed of 100 km/h due north. Winds of 40 km/h travelling due west hit the airplane. What is the new angle the airplane travels in, with respect to the north?

4

Find a Cartesian vector equation for an opposite vector to the one shown in the diagram. Round each coordinate coefficient to an integer.

v = 7i โˆ’ 4j

Find a Cartesian vector equation for an opposite vector to the one shown in the diagram. Round each coordinate coefficient to an integer.

5

Vector v has a magnitude of 30 and makes an angle of 55ยฐ with the y axis. Find the vector equation for v in i, j notation.

v = 24.5i + 17.2j

Vector v has a magnitude of 30 and makes an angle of 55ยฐ with the y axis. Find the vector equation for v in i, j notation.

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