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Vectors- Basics Idea

Vector Quantities:

How to solve:

Sketch the situation and use trigonometry to determine the final location relative to the initial position

Make an accurate scale drawing to determine the final location relative to the initial position

e.g.

Vectors:

Are quantities that have magnitude and direction

e.g. Displacement, velocity, force, acceleration

Scalar:

Quantities that only have magnitude

e.g. distance, speed, magnitude of a force, magnitude of acceleration, energy

Adding Vectors:

We need to draw the lines/ vectors with nose to tail

And then using trigonometry we are able to find the resultant and the direction

e.g.

**Things I Stuggled with , go over again**(3C)

Representing Vectors:

-If we are talking a line from one point (A) to another (B), we represent it by placing a=n arrow on top of both letters.

- If the sides are already lettered, we bold them by underlining them, e.g. vectors a = a

- and for magnitude we write it with | |, e.g. |a|

Equal Vectors:

Two vectors that have the same magnitude and the same direction

The negative of a vector:

Same magnitude but opposite direction

If a = ->AB, then -a = - ->AB = ->BA

Multiplication of a vector by a scalar:

If b=2a then b is the same direction as a but twice the magnitude

Parallel Vectors:

Two vectors that are parallel if one scalar multiple of the other

If the scalar multiple is positive, the vectors are said to be like parallel vectors

If the scalar multiple is negative, the vectors are said to be unlike parallel vectors

Addition of vectors:

Is to add two vectors

And also find the single/ resultant vectors (that replaces the two)

We do this by using a vector triangle

Which the vectors are added from “nose to tail”, which forms two sides of the triangle.

e.g.

Subtraction of one Vector from Another:

Instead of a – b, instead be a + (-b)

With the parallelogram approach one diagonal is a+b and the other is a-b

Also, the triangle inequality is…

The zero Vector:

When we add a vector to the negative of its self we obtain the zero vector:

P+(-P) = 0

-The zero vector has zero magnitude and an undefined direction, we can write the zero vector as 0

ha=kb

a and b are parallel – because one is a scalar multiple of the other)

or h=k=0

e.g. of using sides to describe other sides