2 - VECTORS

• What are scalars?

  Physical quantities described by a single number
• How are scalar quantities of the same kind added?

  Using ordinary arithmetic
• What is the sum of 3s and 5s?

  8s
• What is the sum of 11 kg and 25 kg?

  36 kg
• What are vectors?

  Quantities requiring direction and magnitude
• How are vectors represented visually?

  By an arrow
• What does the direction of the arrow in a vector indicate?

  The direction of the vector
• What does the length of the arrow in a vector represent?

  The magnitude of the vector
• How is the angle measured in vector representation?

  From East to North
• What is a resultant vector?

  A vector sum of two or more vectors
• How does vector addition differ from ordinary addition?

  Vector sum is not ordinary addition
• What is the first step in adding vectors on the same line?

  Specify a positive direction
• How are vectors pointing along the positive direction treated?

  Given a positive algebraic sign
• How are vectors pointing opposite the positive direction treated?

  Given a negative algebraic sign
• What is the vector sum of given vectors?

  The algebraic sum of the vectors
• What sign convention is used for vector components in this course?

  Signs of the Cartesian plane
• What are the signs for the components in Quadrant I?

  (+, +)
• What are the signs for the components in Quadrant II?


  (−, +)
• What are the signs for the components in Quadrant III?

  (−, −)
• What are the signs for the components in Quadrant IV?

  (+, −)
• How is the magnitude of the vector sum obtained for perpendicular vectors?

  Using the Pythagorean theorem
• How is the direction of the resultant vector obtained?

  Using trigonometric functions
• What is the resultant vector formed by two perpendicular vectors?

  The hypotenuse vector
• Given vectors $\mathbf{A} =$$3.0 \text{ m}$ and $\mathbf{B} =$$4.0 \text{ m}$, what is the magnitude of the resultant vector?


  $5.0 \text{ m}$
• How do you solve for the direction of the resultant vector?

  Using $\tan \theta =$$\frac{B}{A}$
• What is the angle $\theta$ when $B =$$4.0 \text{ m}$ and $A =$$3.0 \text{ m}$?


  $53^\circ$
• How is the resultant vector expressed after calculating magnitude and direction?

  $R =$$5.0 \text{ m}, 53^\circ \text{ North of East}$
• What is the first step in adding vectors with arbitrary directions?

  Split each vector into two components
• What do you do after splitting vectors into components?

  Get the vector sum of each component
• What is the final step in adding vectors with arbitrary directions?

  Get the vector sum of the two perpendicular vectors
• Given vectors $\mathbf{A} =$$5.0 \text{ m South}$, $\mathbf{B} =$$3.0 \text{ m North}$, and $\mathbf{C} =$$7.0 \text{ m North}$, what is the resultant vector?


  $5.0 \text{ m North}$
• How do you rewrite vectors using algebraic signs?

  Replace directions with positive or negative signs
• What is the algebraic summation of $-5.0 \text{ m}$, $3.0 \text{ m}$, and $7.0 \text{ m}$?


  $5.0 \text{ m}$
• How do you express the resultant vector after summation?

  Replace the algebraic sign with direction
• What is the first step to find the components of a vector?

  Construct a reference triangle
• What do the corresponding sides of the constructed triangle represent?

  The vector components of the given vector
• How are the magnitudes of vector components obtained?

  Using trigonometric functions
• What is the sine function in relation to a vector?

  $\sin \theta =$$\frac{A_y}{A}$
• What is the cosine function in relation to a vector?

  $\cos \theta =$$\frac{A_x}{A}$
• What does the side opposite to angle $\theta$ represent?


  The side opposite to $\theta$