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Vector vec(a) has an initial point (-2,5) and a terminal point (-5,7). Find the components of vector vec(a). vec(a)=(◻,◻)

Vector a⃗ \vec{a} has an initial point (−2,5) (-2,5) and a terminal point (−5,7) (-5,7) .\newlineFind the components of vector a⃗ \vec{a} .\newlinea⃗=(□,□) \vec{a}=(\square, \square)

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Full solution

Q. Vector a⃗ \vec{a} has an initial point (−2,5) (-2,5) and a terminal point (−5,7) (-5,7) .\newlineFind the components of vector a⃗ \vec{a} .\newlinea⃗=(□,□) \vec{a}=(\square, \square)
  1. Identify initial and terminal points: Identify the initial and terminal points of the vector. The initial point of vector a⃗\vec{a} is (−2,5)(-2,5), and the terminal point is (−5,7)(-5,7).
  2. Calculate change in x-component: Calculate the change in the x-component.\newlineThe change in the x-component (Δx\Delta x) is found by subtracting the x-coordinate of the initial point from the x-coordinate of the terminal point.\newlineΔx=−5−(−2)=−5+2=−3\Delta x = -5 - (-2) = -5 + 2 = -3
  3. Calculate change in y-component: Calculate the change in the y-component.\newlineThe change in the y-component (Δy\Delta y) is found by subtracting the y-coordinate of the initial point from the y-coordinate of the terminal point.\newlineΔy=7−5=2\Delta y = 7 - 5 = 2
  4. Write vector components: Write the components of the vector. The components of vector a⃗\vec{a} are (Δx,Δy)(\Delta x, \Delta y), which we have calculated in the previous steps. a⃗=(−3,2)\vec{a} = (-3, 2)

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