Chapter 10: Q7E (page 549)
Determine the line segment and equivalent representation of
\(\overrightarrow {AB} \).
Short Answer
The equivalent representation point at origin is \(\langle 2,0, - 2\rangle \).
The directed line segment representation and equivalent representation which starts at origin are shown in Figure:
Step by step solution
Given data
Point \(A\) as \((0,3,1)\) and \(B\) as \((2,3, - 1)\).
Concept of vectors
Vector is a quantity that has both magnitude and direction. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude.
Describe the process and draw the Vectors
The points are:\(A(0,3,1),\quad B(2,3, - 1)\)
\(\overrightarrow {AB} \)is the vector from \(A\) to \(B\), to find it, subtract the corresponded components of \(A\) from \(B\).
\({\bf{a}} = \overrightarrow {AB} = < 2 - 0,3 - 3, - 1 - 1 > = < 2,0, - 2 > \)
The equivalent representation starts at the origin is a vector from point \((0,0,0)\) to the point \((2,0, - 2)\).
The directed line segment representation and equivalent representation which starts at origin are shown in Figure:
Describe the process and draw the Vectors
The points are:\(A(0,3,1),\quad B(2,3, - 1)\)
\(\overrightarrow {AB} \)is the vector from \(A\) to \(B\), to find it, subtract the corresponded components of \(A\) from \(B\).
\({\bf{a}} = \overrightarrow {AB} = < 2 - 0,3 - 3, - 1 - 1 > = < 2,0, - 2 > \)
The equivalent representation starts at the origin is a vector from point \((0,0,0)\) to the point \((2,0, - 2)\).
The directed line segment representation and equivalent representation which starts at origin are shown in Figure:
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