Displacement Vectors

A displacement vector shows the change in position from one point to another. To find a displacement vector from an initial point to a terminal point, subtract the coordinates of the initial point from the coordinates of the terminal point. These problems include 2D displacement vectors, 3D displacement vectors, finding initial points, finding terminal points, and using vector notation with \(\vec{i},\vec{j},\vec{k}\).

Notes

Notes for Displacement Vectors

Practice Problems

\(\textbf{1)}\) Find the displacement vector between \(A (-5,8) \) and \( B (6,0)\)Link to Youtube Video Solving Question Number 1

 

\(\textbf{2)}\) Find the displacement vector between \(A (4,2) \) and \( B (1,9)\)

 

\(\textbf{3)}\) Find the displacement vector between \(A (0,0) \) and \( B (1,5)\)

 

\(\textbf{4)}\) Find the displacement vector between \(C (1,3,2) \) and \( D (4,-1,-5)\)Link to Youtube Video Solving Question Number 4

 

\(\textbf{5)}\) Find the displacement vector between \(C (5,1,6) \) and \( D (-3,-2,-1)\)

 

\(\textbf{6)}\) Find the displacement vector between \(C (1,2,3) \) and \( D (4,-5,-6)\)

 

\(\textbf{7)}\) Find the initial point \((P)\) of vector \(\vec{v}\) from \(P\) to \(Q\) where \(\vec{v}= \langle3,8\rangle \) and \( Q= (4,1)\)

 

\(\textbf{8)}\) Find the initial point \((P)\) of vector \(\vec{v}\) from \(P\) to \(Q\) where \(\vec{v}= \langle-5,2\rangle \) and \( Q= (3,-1)\)

 

\(\textbf{9)}\) Find the initial point \((P)\) of vector \(\vec{v}\) from \(P\) to \(Q\) where \(\vec{v}= \langle-4,0\rangle \) and \( Q= (9,9)\)

 

\(\textbf{10)}\) Find the displacement vector between \(A (-2,-3) \) and \( B (5,9)\)

 

\(\textbf{11)}\) Find the displacement vector between \(A (10,-4) \) and \( B (-2,1)\)

 

\(\textbf{12)}\) Find the displacement vector between \(C (-1,4,7) \) and \( D (2,-6,10)\)

 

\(\textbf{13)}\) Find the displacement vector between \(C (8,0,-5) \) and \( D (-1,6,2)\)

 

\(\textbf{14)}\) Find the terminal point \((Q)\) of vector \(\vec{v}\) from \(P\) to \(Q\) where \(\vec{v}= \langle4,-6\rangle \) and \( P= (-2,5)\)

 

\(\textbf{15)}\) Find the terminal point \((Q)\) of vector \(\vec{v}\) from \(P\) to \(Q\) where \(\vec{v}= \langle-3,7\rangle \) and \( P= (6,-2)\)

 

Challenge Problems

\(\textbf{16)}\) Find the initial point \((P)\) of vector \(\vec{v}\) from \(P\) to \(Q\) where \(\vec{v}= \langle2,-5,4\rangle \) and \( Q= (7,-1,10)\)

 

\(\textbf{17)}\) Find the terminal point \((Q)\) of vector \(\vec{v}\) from \(P\) to \(Q\) where \(\vec{v}= \langle-4,3,-8\rangle \) and \( P= (2,5,1)\)

 

\(\textbf{18)}\) Find \(k\) if the displacement vector from \(A(2,k)\) to \(B(9,4)\) is \(\langle7,-3\rangle\).

 

\(\textbf{19)}\) Find \(k\) if the displacement vector from \(A(-1,5,2)\) to \(B(3,k,-4)\) is \(\langle4,-8,-6\rangle\).

 

\(\textbf{20)}\) Find the midpoint of the segment from \(A(-5,8)\) to \(B(6,0)\) using the displacement vector.

 

 

See Related Pages\(\)

\(\bullet\text{ Displacement Vectors}\)
\(\,\,\,\,\,\,\,\,(x_2-x_1)\vec{i}+(y_2-y_1)\vec{j}…\)
\(\bullet\text{ Magnitude, Direction, and Unit Vectors}\)
\(\,\,\,\,\,\,\,\,|\vec{u}|=\sqrt{a^2+b^2}…\)
\(\bullet\text{ Dot Product}\)
\(\,\,\,\,\,\,\,\,a \cdot b=x_1 x_2+ y_1 y_2…\)
\(\bullet\text{ Parallel and Perpendicular Vectors}\)
\(\,\,\,\,\,\,\,\,⟨8,2⟩ \text{ and } ⟨−4,−1⟩…\)
\(\bullet\text{ Scalar and Vector Projections}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{a \cdot b}{|b|^2} \, \vec{b}…\)
\(\bullet\text{ Cross Product}\)
\(\,\,\,\,\,\,\,\,\)Thumbnail for Cross Product\(…\)
\(\bullet\text{ Equation of a Plane}\)
\(\,\,\,\,\,\,\,\,Ax+By+Cz=D…\)

 

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