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Mathematics 1
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səhifə | 1/5 | tarix | 26.10.2023 | ölçüsü | 1,08 Mb. | | #131170 |
| Vectors Vectors Definitions - A scalar is a quantity which has magnitude only, e.g., temperature, mass, pressure.
- A vector is a quantity which has both: a magnitude and a direction e.g., displacement,
- velocity, magnetic field.
- The directed line segment
- -represents a vector
- The length PQ- its magnitude
- Notations of vectors: ; ; ;
- Notations of magnitudes:|a| or ||a||
P
Q
The triangle rule.
We can add two vectors by joining them head-to-tail:
it doesn't matter which order we add them, we get the same result:
This rule for adding vectors represented by line segments is called the triangle rule.
a + b = b + a
Subtraction of vectors
- -A is defined to be the vector with the same magnitude as A but opposite direction.
- 0 is the zero vector (or null vector) with zero magnitude and any direction.
To subtract, first reverse the vector we want to subtract, then add using the triangle rule
Sample problem 1
Write as single vectors:
Answer:
Multiplication by scalars - We can multiply vectors by scalars (i.e. numbers).
- When p > 0, pa is defined to be the vector
with the same direction as and p times the magnitude of a. - When p < 0, pa is the vector with the opposite direction to a and -p = times the magnitude.
- Pictorially this looks like stretching or squeezing the vector.
- When we multiply a vector by a scalar it is called "scaling" a vector, because we change how big or small the vector is.
- A vector of magnitude one is
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