|definition||a quantity that has
|a quantity that has both
magnitude and direction
|up, down, left, right
north, east, west, south
positive, negative (in a coordinate system)
angle of inclination, depression
angle with the vertical, horizontal
right ascension, declination
proper time (relativistic)
electric, magnetic, gravitational fields
vector addition, vector subtraction
resultant (Σ), change (Δ)
dot product (·), cross product (×)
|answers||a number with a unit||a number with a unit and a direction angle
a number with a unit along each coordinate axis
an arrow drawn to scale in a specific direction
Jump off the line.
Don't forget the parallelogram rule.
Lot's of vectors to be added.
Conclude and get on with the sample problems.
|45°, 45°, 90°
1 : 1 : √(2)
|An isosceles right triangle. The two legs are equal in size. If we assume each leg has a length of one, according to Pythagoras' theorem, the hypotenuse has a length equal to the square root of two.|
|30°, 60°, 90°
1 : 2 : √(3)
|Half an equilateral triangle. Assume the sides of the full triangle have a length of two. Split it in half and the side opposite the 30° angle has a length of one. Using Pythagoras' theorem, the remaining leg has a length equal to the square root of three.|
|37°, 53°, 90°
3 : 4 : 5
|The simplest Pythagorean triple. The size of the angles are best determined with a calculator. Standardized tests love this triangle. (Secret reason: It simplifies grading.) Some people memorize these angles to help them spot 3-4-5 triangles on tests.|
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