T1W6L2: Vectors

vectors §

• A vector is a quantity with magnitude and direction.
• e.g. a measurement of distance travelled such as 10km is not a vector quantity.
• ways of representing vector.
  • specifications of magnitude and direction e.g. 10km at $030°$
  • an arrow (usually drawn to scales)
  • component form e.g. $\left(\genfrac{}{}{0ex}{}{8.6}{5}\right)$ or $<8.6,5>$
• sadler 3a: basically bearing questions, need to use non-right triangle trignometry.
  • e.g.
    • a boat sails 15km on a bearing of $170°$ followed by 9km due East. Find the distance and bearing of the boats’ final direction from its initial position.
    • solution:
      • method one: by calculation
      • if a is the initial position and C is the final position then the distance from A to C is given by AC.
      • now $A{C}^2=15^2+9^2-2\times 15\times 9\times \cos (100°)$ (cos rule)
      • the bearing of C from A is ($170°$ - $\angle BAC$)
• sadler 3b
  • obtaining a resultant force vector from two force vectors acting together.
  • e.g. two forces act on a weight as shown. Find the resultant force vector.
  • very important that finding the resultant of two force vectors is not simply adding magnitude and direction, only applicable if both vectors are in the exact direction, such the resultant needs to be derived from trig through the stratergy of adding vectors.

other vector notes: T1W7L2: vector in component form T1W6L3: vectors continued some other ones icbb to find