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Vector 
vec(b) has an initial point 
(-2,7) and a terminal point 
(9,4).
Find the components of vector 
vec(b).

vec(b)=(◻,◻)

Vector b \vec{b} has an initial point (2,7) (-2,7) and a terminal point (9,4) (9,4) .\newlineFind the components of vector b \vec{b} .\newlineb=,) \vec{b}=\square, \square)

Full solution

Q. Vector b \vec{b} has an initial point (2,7) (-2,7) and a terminal point (9,4) (9,4) .\newlineFind the components of vector b \vec{b} .\newlineb=,) \vec{b}=\square, \square)
  1. Identify initial and terminal points: Identify the initial and terminal points of the vector. The initial point of vector b\vec{b} is (2,7)(-2,7), and the terminal point is (9,4)(9,4). To find the components of the vector, we need to subtract the coordinates of the initial point from the coordinates of the terminal point.
  2. Calculate horizontal component: Calculate the horizontal component of the vector.\newlineThe horizontal component is found by subtracting the xx-coordinate of the initial point from the xx-coordinate of the terminal point.\newlineHorizontal component = xterminalxinitial=9(2)=9+2=11x_{\text{terminal}} - x_{\text{initial}} = 9 - (-2) = 9 + 2 = 11
  3. Calculate vertical component: Calculate the vertical component of the vector. The vertical component is found by subtracting the yy-coordinate of the initial point from the yy-coordinate of the terminal point. Vertical component = yterminalyinitial=47=3y_{\text{terminal}} - y_{\text{initial}} = 4 - 7 = -3
  4. Combine components to form vector: Combine the horizontal and vertical components to form the vector components.\newlineThe components of vector b\vec{b} are (horizontal component, vertical component), which is (11,3)(11, -3).

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