Find a vector a with representation given by the directed line segment AB. Draw AB and the equivalent representation starting at the origin. A(−2,I), B(l,2)

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Find a vector a with representation given by the directed line segment AB. Draw AB and the equivalent representation starting at the origin.  A(−2,I), B(l,2)

Laura Worden · Accepted Answer

Given A(−1,1), B(3,2)    Substract the corresponding components of A and B    a=AB→=&amp;lt;3−(−1),2−1≥&amp;lt;4,1&amp;gt;    The equivalent representation is a vector from the point (0,0) to (4,1)

user_27qwe · Accepted Answer

To find the vector a→ with the representation given by the directed line segment AB, where A(−2,1) and B(1,2), we can use the formula:a→=B→−A→Substituting the values of A and B, we have:a→=[12]−[−21]Simplifying the subtraction, we get:a→=[1−(−2)2−1]Thus, the vector a→ is:a→=[31]Now, let&#039;s draw the line segment AB and the equivalent representation of a→ starting at the origin.[Drawing]As shown in the drawing, the line segment AB extends from the point A(−2,1) to the point B(1,2). The vector a→ with representation starting at the origin is represented by the arrow starting at the origin and ending at the point (3,1).

karton · Accepted Answer

Step 1:The vector representation of a line segment from point A to point B is given by the difference between the coordinates of B and A. Therefore, the vector 𝐚 can be found as:𝐚=𝐁−𝐀Given that point A is A(−2,1) and point B is B(1,2), we can calculate the vector 𝐚 as:𝐚=(12)−(−21)Simplifying this expression, we get:𝐚=(1+22−1)𝐚=(31)Step 2:Now, let&#039;s draw the directed line segment AB and the vector representation starting from the origin.AB:To draw AB, we start at point A (−2,1) and end at point B (1,2).AB→:To draw the vector representation AB→ starting from the origin, we start at the origin (0,0) and end at the coordinates of B (1,2).Now, let&#039;s visualize this on a coordinate plane:AB:- Draw a line segment from point A (−2,1) to point B (1,2).AB→:- Draw an arrow starting from the origin (0,0) and ending at the coordinates of B (1,2).By following these steps, you should be able to solve the problem and draw the directed line segment AB and its equivalent vector representation starting from the origin.

Find a vector a with representation given by the directed

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