The value of k is 2/5
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Further explanation
Vector is quantity that has magnitude and direction.
One example of a vector is acceleration.
Let us now tackle the problem !
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This problem is about Vector Diagram.
[tex]\overrightarrow{OA} = \overrightarrow{a}[/tex]
[tex]\overrightarrow{OC} = \overrightarrow{c}[/tex]
X is the midpoint of the line AC:
[tex]\overrightarrow{x} = \frac{1}{2} (\overrightarrow{a} + \overrightarrow{c})[/tex]
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OC : CD = k : 1
[tex]k \overrightarrow{CD} = \overrightarrow{OC}}[/tex]
[tex]k( \overrightarrow{d} - \overrightarrow{c} ) = \overrightarrow{c}}[/tex]
[tex]( \overrightarrow{d} - \overrightarrow{c} ) = \frac{1}{k} \overrightarrow{c}}[/tex]
[tex]\overrightarrow{d} = \overrightarrow{c} + \frac{1}{k} \overrightarrow{c}}[/tex]
[tex]\overrightarrow{d} = ( 1 + \frac{1}{k} ) \overrightarrow{c}}[/tex]
[tex]\texttt{ }[/tex]
[tex]\overrightarrow{XD} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}[/tex]
[tex]\overrightarrow{d} - \overrightarrow{x} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}[/tex]
[tex]( 1 + \frac{1}{k} ) \overrightarrow{c} - \frac{1}{2} (\overrightarrow{a} + \overrightarrow{c}) = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}[/tex]
[tex]( 1 + \frac{1}{k} - \frac{1}{2}) \overrightarrow{c} - \frac{1}{2} \overrightarrow{a} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}[/tex]
[tex]( \frac{1}{k} + \frac{1}{2}) \overrightarrow{c} - \frac{1}{2} \overrightarrow{a} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}[/tex]
[tex]\frac{1}{k} + \frac{1}{2} = 3[/tex]
[tex]\frac{1}{k} = 3 - \frac{1}{2}[/tex]
[tex]\frac{1}{k} = \frac{5}{2}[/tex]
[tex]k = \frac{2}{5}[/tex]
[tex]\texttt{ }[/tex]
Learn more
- Velocity of Runner : https://brainly.com/question/3813437
- Kinetic Energy : https://brainly.com/question/692781
- Acceleration : https://brainly.com/question/2283922
- The Speed of Car : https://brainly.com/question/568302
Answer details
Grade: High School
Subject: Mathematics
Chapter: Vectors
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate, Stream , Vector
