Points, Arrows, Vectors: Exercises

Problem 1

For each of the following pairs of points \(A\) and \(B\) find the vector \(\Vect{x}\) represented by the arrow \(\Arrow{A}{B}\)

  1. \(A(6,1)\) and \(B(9,4)\)

  2. \(A(2,-3,5)\) and \(B(7,-4,1)\)

  3. \(A(1,3,-2)\) and \(B(6,2,-2)\)

  4. \(A(-2,0,6,-4)\) and \(B(2,-2,-6,2)\)

  5. \(A(9,12,17,-15,-3)\) and \(B(-9,21,-16,4,-1)\)

Problem 2

For the given vector and tail point \(A\), find the tip \(B\) of the arrow \(\Arrow{A}{B}\) representing the vector.

  1. \(\Vect{x}=(4,1)\) and \(A(4,6)\)

  2. \(\Vect{y} = (1,-3,2)\) and \(A(1,1,1)\)

  3. \(\Vect{z} = (6,-2,4,-1)\) and \(A(2,1,2,1)\)

  4. \(\Vect{a} = (-7,2,0,1,-3))\) and \(A(6,4,1,0,-3)\)

  5. \(\Vect{b} = (15,-12,20,9,7,3)\) and \(A(23,18,-18,6,14,4)\)

  6. \(\Vect{u}=(x,y,z)\) and \(A(4,1,7)\)

Problem 3

For the given vector and tip point \(B\), find the tail \(A\) of the arrow representing the vector.

  1. \(\Vect{x}=(1,1)\) and \(B(3,4)\)

  2. \(\Vect{y} = (6,-3,1)\) and \(B(3,3,3)\)

  3. \(\Vect{z} = (1,-1,4,-2)\) and \(B(0,1,-2,1)\)

  4. \(\Vect{a} = (6,-6,3,1,-5)\) and \(B(1,2,-1,0,6)\)

  5. \(\Vect{b} = (-6,15,-22,6,5,3)\) and \(B(41,12,21,-36,9,-4)\)

  6. \(\Vect{c}=(u,v,w)\) and \(B(2,a,x)\)