Physics

• it comes from a Greek word which means knowledge of nature
• study of matter in relation to energy
• scalar quantities is refer to quantities that require only the magnitude
• vector quantities required both magnitude and direction
• arrowhead signifies direction
• length signifies magnitude
• north is located at the top
• south is located at the bottom
• on the left side, west is there
• right side is east
• Equality of vectors are equal if the have the same magnitude and direction
• negative of a vector is a=5m, NE -a=5m, SW
• a + b = b + a is an example of commutative property of vector addition
• (a+b)+c = a(b+c) is associative property for vector addition
• an example of distributive property is c(a+b)=ca+cb where c is a constant
• Graphical method are tail-tip method, polygon method, parallelogram method
• two types of vector addition is graphical and analytical method
• analytical vector addition are pythagorean theorem, trigonometric function, sine law, cosine law
• c = sqrt of a^2+b^2
• sin = o/h
• cos = a/h
• tan = o/a
• x in x components uses cos
• y in y components uses sin
• to get the summation, add the answer from dx and dy
• resultant is sqrt of 2dx^2+2dy^2
• direction uses arctan = dy/dx
• the purpose of unit vector is to describe a direction in space
• in unit vectors, it will include the caret or hat in the symbol to distinguish from ordinary vectors whose magnitude may or may bot be 1
• product of a dot product is a scalar quantity
• the dot product of a and b is equal to product of their magnitude of the component of b that is parallel to a
• i . i = cos0 = 1
• j . j = cos0 = 1
• k.k = cos0=1
• -k . -k = cos0 = 1
• -i . i = cos180 = -1
• k . -k cos180 = -1
• i . j = cos90 = 0
• -j . k = cos90 = 0
• a = 2i + 3j + 4k

  b = -3i + 2j - 4k

  a . b = -6i + 6 - 16

  a . b = 0